exp_final_3_attr – Complete Experiment Report

three_attr_corr

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Vary_Correlation_with_Dim_and_Tails (MvStudentT, correlation, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 3.482 0.00341 5.446
HMC 0.3 1.243 0.234 3.099
HMC 0.5 4.124 0.000807 4.231
HMC 0.9 3.416 0.00406 8.348
HMC 0.95 4.588 0.000365 6.937
HMC 0.99 1.828 0.089 28.095
SMC 0.0 12.093 6.81e-12 5.516
SMC 0.3 10.148 2.47e-09 6.113
SMC 0.5 6.612 6.86e-06 7.399
SMC 0.9 7.276 3.38e-06 14.995
SMC 0.95 5.798 4.1e-05 12.297
SMC 0.99 7.415 2.49e-06 12.599
Metro 0.0 4.210 0.000829 9.775
Metro 0.3 6.224 2.22e-05 118.345
Metro 0.5 1.963 0.0699 49.897
Metro 0.9 3.331 0.00495 1063.931
Metro 0.95 4.907 0.000231 1991.710
Metro 0.99 6.549 1.29e-05 1322.529
DEMetro_Z 0.0 18.060 4.24e-11 339.028
DEMetro_Z 0.3 7.515 2.81e-06 1628.986
DEMetro_Z 0.5 10.687 4.07e-08 426.333
DEMetro_Z 0.9 10.204 7.27e-08 1693.544
DEMetro_Z 0.95 23.426 1.25e-12 3020.480
DEMetro_Z 0.99 8.019 1.33e-06 1013.809
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -17.537 6.34e-11 -4.528
HMC_vs_DEMetro_Z 0.3 -7.488 2.93e-06 -1.933
HMC_vs_DEMetro_Z 0.5 -10.748 3.8e-08 -2.775
HMC_vs_DEMetro_Z 0.9 -10.158 7.69e-08 -2.623
HMC_vs_DEMetro_Z 0.95 -23.438 1.24e-12 -6.052
HMC_vs_DEMetro_Z 0.99 -7.793 1.86e-06 -2.012
Metro_vs_SMC 0.0 1.752 0.102 0.452
Metro_vs_SMC 0.3 5.857 4.17e-05 1.512
Metro_vs_SMC 0.5 1.670 0.117 0.431
Metro_vs_SMC 0.9 3.281 0.00547 0.847
Metro_vs_SMC 0.95 4.885 0.000241 1.261
Metro_vs_SMC 0.99 6.460 1.5e-05 1.668
Metro_vs_DEMetro_Z 0.0 -17.595 6.06e-11 -4.543
Metro_vs_DEMetro_Z 0.3 -7.030 5.96e-06 -1.815
Metro_vs_DEMetro_Z 0.5 -7.740 2.01e-06 -1.998
Metro_vs_DEMetro_Z 0.9 -1.585 0.135 -0.409
Metro_vs_DEMetro_Z 0.95 -2.659 0.0187 -0.687
Metro_vs_DEMetro_Z 0.99 1.541 0.146 0.398
HMC_vs_Metro 0.0 -2.146 0.0499 -0.554
HMC_vs_Metro 0.3 -5.993 3.29e-05 -1.547
HMC_vs_Metro 0.5 -1.804 0.0928 -0.466
HMC_vs_Metro 0.9 -3.307 0.00519 -0.854
HMC_vs_Metro 0.95 -4.888 0.000239 -1.262
HMC_vs_Metro 0.99 -6.359 1.77e-05 -1.642
HMC_vs_SMC 0.0 -0.041 0.968 -0.011
HMC_vs_SMC 0.3 -1.122 0.281 -0.290
HMC_vs_SMC 0.5 -1.919 0.0755 -0.496
HMC_vs_SMC 0.9 -2.238 0.042 -0.578
HMC_vs_SMC 0.95 -1.885 0.0804 -0.487
HMC_vs_SMC 0.99 1.026 0.322 0.265
DEMetro_Z_vs_SMC 0.0 17.790 5.23e-11 4.593
DEMetro_Z_vs_SMC 0.3 7.484 2.95e-06 1.932
DEMetro_Z_vs_SMC 0.5 10.474 5.25e-08 2.704
DEMetro_Z_vs_SMC 0.9 10.159 7.68e-08 2.623
DEMetro_Z_vs_SMC 0.95 23.280 1.36e-12 6.011
DEMetro_Z_vs_SMC 0.99 7.910 1.56e-06 2.042
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.203 0.067 0.025 5.446
HMC 0.3 0.143 0.075 0.022 3.099
HMC 0.5 0.182 0.069 0.027 4.231
HMC 0.9 0.251 0.041 0.025 8.348
HMC 0.95 0.272 0.053 0.032 6.937
HMC 0.99 0.907 0.049 0.031 28.095
SMC 0.0 0.204 0.067 0.025 5.516
SMC 0.3 0.209 0.075 0.022 6.113
SMC 0.5 0.266 0.069 0.027 7.399
SMC 0.9 0.418 0.041 0.025 14.995
SMC 0.95 0.441 0.053 0.032 12.297
SMC 0.99 0.434 0.049 0.031 12.599
Metro 0.0 0.310 0.067 0.025 9.775
Metro 0.3 2.664 0.075 0.022 118.345
Metro 0.5 1.396 0.069 0.027 49.897
Metro 0.9 26.745 0.041 0.025 1063.931
Metro 0.95 62.900 0.053 0.032 1991.710
Metro 0.99 40.439 0.049 0.031 1322.529
DEMetro_Z 0.0 8.483 0.067 0.025 339.028
DEMetro_Z 0.3 35.709 0.075 0.022 1628.986
DEMetro_Z 0.5 11.406 0.069 0.027 426.333
DEMetro_Z 0.9 42.548 0.041 0.025 1693.544
DEMetro_Z 0.95 95.363 0.053 0.032 3020.480
DEMetro_Z 0.99 31.010 0.049 0.031 1013.809
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.524 0.607 -0.140
HMC 0.3 0.864 0.401 1.415
HMC 0.5 1.198 0.242 0.559
HMC 0.9 1.508 0.154 6.294
HMC 0.95 1.837 0.079 0.907
HMC 0.99 1.056 0.309 16.183
SMC 0.0 16.406 3.61e-12 4.516
SMC 0.3 31.921 2.8e-19 9.280
SMC 0.5 30.803 1.85e-20 15.057
SMC 0.9 20.735 5.62e-12 80.422
SMC 0.95 16.536 1.25e-10 72.022
SMC 0.99 22.920 4.14e-13 31.307
Metro 0.0 1.498 0.15 0.901
Metro 0.3 3.273 0.00555 51.501
Metro 0.5 1.066 0.304 18.462
Metro 0.9 2.255 0.0407 1860.157
Metro 0.95 2.915 0.0113 6337.944
Metro 0.99 3.961 0.00142 776.632
DEMetro_Z 0.0 14.134 9.53e-10 46.915
DEMetro_Z 0.3 12.174 7.77e-09 938.389
DEMetro_Z 0.5 8.800 4.35e-07 63.676
DEMetro_Z 0.9 12.024 9.12e-09 821.982
DEMetro_Z 0.95 10.092 8.34e-08 2048.383
DEMetro_Z 0.99 6.837 8.09e-06 176.377
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -29.434 5.43e-14 -7.600
HMC_vs_SMC 0.3 -4.900 0.000234 -1.265
HMC_vs_SMC 0.5 -20.325 8.64e-12 -5.248
HMC_vs_SMC 0.9 -10.531 4.9e-08 -2.719
HMC_vs_SMC 0.95 -16.225 1.79e-10 -4.189
HMC_vs_SMC 0.99 -1.007 0.331 -0.260
Metro_vs_DEMetro_Z 0.0 -13.846 1.46e-09 -3.575
Metro_vs_DEMetro_Z 0.3 -11.006 2.81e-08 -2.842
Metro_vs_DEMetro_Z 0.5 -2.673 0.0182 -0.690
Metro_vs_DEMetro_Z 0.9 1.230 0.239 0.318
Metro_vs_DEMetro_Z 0.95 2.068 0.0576 0.534
Metro_vs_DEMetro_Z 0.99 3.112 0.00765 0.803
HMC_vs_Metro 0.0 -1.911 0.0767 -0.493
HMC_vs_Metro 0.3 -3.106 0.00773 -0.802
HMC_vs_Metro 0.5 -1.031 0.32 -0.266
HMC_vs_Metro 0.9 -2.246 0.0414 -0.580
HMC_vs_Metro 0.95 -2.915 0.0113 -0.753
HMC_vs_Metro 0.99 -3.834 0.00182 -0.990
HMC_vs_DEMetro_Z 0.0 -14.278 9.76e-10 -3.686
HMC_vs_DEMetro_Z 0.3 -12.073 8.65e-09 -3.117
HMC_vs_DEMetro_Z 0.5 -8.823 4.31e-07 -2.278
HMC_vs_DEMetro_Z 0.9 -11.782 1.18e-08 -3.042
HMC_vs_DEMetro_Z 0.95 -10.086 8.41e-08 -2.604
HMC_vs_DEMetro_Z 0.99 -5.098 0.000162 -1.316
Metro_vs_SMC 0.0 -6.377 1.72e-05 -1.647
Metro_vs_SMC 0.3 2.668 0.0184 0.689
Metro_vs_SMC 0.5 0.198 0.846 0.051
Metro_vs_SMC 0.9 2.155 0.049 0.557
Metro_vs_SMC 0.95 2.882 0.0121 0.744
Metro_vs_SMC 0.99 3.798 0.00196 0.981
DEMetro_Z_vs_SMC 0.0 12.762 4.23e-09 3.295
DEMetro_Z_vs_SMC 0.3 12.047 8.89e-09 3.111
DEMetro_Z_vs_SMC 0.5 6.881 7.55e-06 1.777
DEMetro_Z_vs_SMC 0.9 10.961 2.96e-08 2.830
DEMetro_Z_vs_SMC 0.95 9.657 1.44e-07 2.493
DEMetro_Z_vs_SMC 0.99 5.577 6.82e-05 1.440
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 5.754 8.592 20.294 -0.140
HMC 0.3 25.906 9.988 11.248 1.415
HMC 0.5 12.393 8.128 7.632 0.559
HMC 0.9 16.869 3.153 2.179 6.294
HMC 0.95 5.960 3.562 2.643 0.907
HMC 0.99 101.608 5.818 5.919 16.183
SMC 0.0 100.231 8.592 20.294 4.516
SMC 0.3 114.368 9.988 11.248 9.280
SMC 0.5 123.039 8.128 7.632 15.057
SMC 0.9 178.410 3.153 2.179 80.422
SMC 0.95 193.933 3.562 2.643 72.022
SMC 0.99 191.130 5.818 5.919 31.307
Metro 0.0 26.877 8.592 20.294 0.901
Metro 0.3 589.249 9.988 11.248 51.501
Metro 0.5 149.018 8.128 7.632 18.462
Metro 0.9 4056.818 3.153 2.179 1860.157
Metro 0.95 16756.253 3.562 2.643 6337.944
Metro 0.99 4602.850 5.818 5.919 776.632
DEMetro_Z 0.0 960.659 8.592 20.294 46.915
DEMetro_Z 0.3 10564.664 9.988 11.248 938.389
DEMetro_Z 0.5 494.072 8.128 7.632 63.676
DEMetro_Z 0.9 1794.421 3.153 2.179 821.982
DEMetro_Z 0.95 5417.927 3.562 2.643 2048.383
DEMetro_Z 0.99 1049.826 5.818 5.919 176.377
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 5.406 8.07e-05 9.924
HMC 0.3 2.687 0.0177 17.838
HMC 0.5 5.253 0.000113 12.408
HMC 0.9 5.375 9.72e-05 42.293
HMC 0.95 7.408 2.97e-06 20.185
HMC 0.99 1.711 0.109 60.822
SMC 0.0 123.443 2.49e-23 239.156
SMC 0.3 119.537 8.97e-23 339.492
SMC 0.5 92.518 4.7e-21 369.737
SMC 0.9 54.403 1.06e-17 927.278
SMC 0.95 38.499 1.29e-15 504.847
SMC 0.99 55.549 7.51e-18 434.204
Metro 0.0 3.204 0.00636 44.403
Metro 0.3 7.066 5.63e-06 447.380
Metro 0.5 1.971 0.0688 93.590
Metro 0.9 4.804 0.00028 3156.771
Metro 0.95 6.067 2.9e-05 3975.624
Metro 0.99 8.407 7.65e-07 2287.905
DEMetro_Z 0.0 29.445 5.37e-14 779.549
DEMetro_Z 0.3 21.710 3.53e-12 3721.644
DEMetro_Z 0.5 23.667 1.08e-12 851.353
DEMetro_Z 0.9 17.458 6.73e-11 4565.295
DEMetro_Z 0.95 28.938 6.86e-14 4871.482
DEMetro_Z 0.99 12.929 3.57e-09 1573.929
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -25.372 4.18e-13 -6.551
Metro_vs_DEMetro_Z 0.3 -18.618 2.83e-11 -4.807
Metro_vs_DEMetro_Z 0.5 -13.342 2.37e-09 -3.445
Metro_vs_DEMetro_Z 0.9 -1.766 0.0991 -0.456
Metro_vs_DEMetro_Z 0.95 -1.486 0.16 -0.384
Metro_vs_DEMetro_Z 0.99 3.298 0.00528 0.852
DEMetro_Z_vs_SMC 0.0 20.465 7.87e-12 5.284
DEMetro_Z_vs_SMC 0.3 19.636 1.38e-11 5.070
DEMetro_Z_vs_SMC 0.5 13.731 1.63e-09 3.545
DEMetro_Z_vs_SMC 0.9 13.694 1.69e-09 3.536
DEMetro_Z_vs_SMC 0.95 24.905 5.4e-13 6.430
DEMetro_Z_vs_SMC 0.99 9.316 2.23e-07 2.405
HMC_vs_DEMetro_Z 0.0 -29.541 5.16e-14 -7.627
HMC_vs_DEMetro_Z 0.3 -21.517 3.98e-12 -5.556
HMC_vs_DEMetro_Z 0.5 -24.116 8.39e-13 -6.227
HMC_vs_DEMetro_Z 0.9 -17.604 6.02e-11 -4.545
HMC_vs_DEMetro_Z 0.95 -28.747 7.51e-14 -7.423
HMC_vs_DEMetro_Z 0.99 -11.931 1.01e-08 -3.081
HMC_vs_Metro 0.0 -2.552 0.023 -0.659
HMC_vs_Metro 0.3 -6.589 1.21e-05 -1.701
HMC_vs_Metro 0.5 -1.712 0.109 -0.442
HMC_vs_Metro 0.9 -4.731 0.000322 -1.222
HMC_vs_Metro 0.95 -6.030 3.09e-05 -1.557
HMC_vs_Metro 0.99 -8.008 1.35e-06 -2.068
HMC_vs_SMC 0.0 -72.318 2.03e-19 -18.672
HMC_vs_SMC 0.3 -50.525 3.02e-17 -13.046
HMC_vs_SMC 0.5 -76.254 9.67e-20 -19.689
HMC_vs_SMC 0.9 -41.201 5.15e-16 -10.638
HMC_vs_SMC 0.95 -33.825 7.94e-15 -8.734
HMC_vs_SMC 0.99 -10.925 3.09e-08 -2.821
Metro_vs_SMC 0.0 -13.758 1.59e-09 -3.552
Metro_vs_SMC 0.3 1.654 0.12 0.427
Metro_vs_SMC 0.5 -5.873 4.05e-05 -1.516
Metro_vs_SMC 0.9 3.365 0.00463 0.869
Metro_vs_SMC 0.95 5.290 0.000114 1.366
Metro_vs_SMC 0.99 6.794 8.68e-06 1.754
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.392 0.114 0.028 9.924
HMC 0.3 0.498 0.121 0.021 17.838
HMC 0.5 0.373 0.118 0.021 12.408
HMC 0.9 0.511 0.094 0.010 42.293
HMC 0.95 0.467 0.094 0.018 20.185
HMC 0.99 1.401 0.095 0.021 60.822
SMC 0.0 6.811 0.114 0.028 239.156
SMC 0.3 7.293 0.121 0.021 339.492
SMC 0.5 7.707 0.118 0.021 369.737
SMC 0.9 9.238 0.094 0.010 927.278
SMC 0.95 9.431 0.094 0.018 504.847
SMC 0.99 9.418 0.095 0.021 434.204
Metro 0.0 1.357 0.114 0.028 44.403
Metro 0.3 9.572 0.121 0.021 447.380
Metro 0.5 2.039 0.118 0.021 93.590
Metro 0.9 31.222 0.094 0.010 3156.771
Metro 0.95 73.624 0.094 0.018 3975.624
Metro 0.99 49.219 0.095 0.021 2287.905
DEMetro_Z 0.0 21.943 0.114 0.028 779.549
DEMetro_Z 0.3 78.745 0.121 0.021 3721.644
DEMetro_Z 0.5 17.593 0.118 0.021 851.353
DEMetro_Z 0.9 45.112 0.094 0.010 4565.295
DEMetro_Z 0.95 90.193 0.094 0.018 4871.482
DEMetro_Z 0.99 33.890 0.095 0.021 1573.929
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 5.478 8.13e-05 93.785
HMC 0.3 2.777 0.0148 34.250
HMC 0.5 5.567 6.83e-05 30.617
HMC 0.9 6.562 1.1e-05 14.058
HMC 0.95 7.821 1.42e-06 15.262
HMC 0.99 7.587 2.29e-06 22.015
SMC 0.0 133.209 2e-23 389.020
SMC 0.3 98.337 1.26e-21 254.362
SMC 0.5 144.843 1.04e-24 227.375
SMC 0.9 73.527 2.59e-21 80.078
SMC 0.95 63.337 1.41e-19 90.525
SMC 0.99 75.373 1.82e-21 82.402
Metro 0.0 6.368 1.74e-05 165.415
Metro 0.3 34.285 6.31e-15 299.276
Metro 0.5 7.242 4.26e-06 108.097
Metro 0.9 27.196 1.36e-13 112.510
Metro 0.95 34.705 4.45e-15 133.372
Metro 0.99 47.287 4.77e-17 137.072
DEMetro_Z 0.0 59.752 2.73e-18 493.416
DEMetro_Z 0.3 36.667 2.5e-15 344.321
DEMetro_Z 0.5 32.080 1.6e-14 319.232
DEMetro_Z 0.9 22.355 2.18e-12 123.920
DEMetro_Z 0.95 40.416 5.31e-16 157.807
DEMetro_Z 0.99 21.986 2.76e-12 126.928
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 11.643 1.38e-08 3.006
DEMetro_Z_vs_SMC 0.3 8.948 3.63e-07 2.310
DEMetro_Z_vs_SMC 0.5 9.000 3.39e-07 2.324
DEMetro_Z_vs_SMC 0.9 7.272 4.08e-06 1.878
DEMetro_Z_vs_SMC 0.95 16.745 1.18e-10 4.324
DEMetro_Z_vs_SMC 0.99 7.583 2.54e-06 1.958
HMC_vs_Metro 0.0 -2.724 0.0165 -0.703
HMC_vs_Metro 0.3 -17.967 4.58e-11 -4.639
HMC_vs_Metro 0.5 -4.802 0.000281 -1.240
HMC_vs_Metro 0.9 -23.511 1.19e-12 -6.071
HMC_vs_Metro 0.95 -28.714 7.64e-14 -7.414
HMC_vs_Metro 0.99 -27.913 1.13e-13 -7.207
Metro_vs_DEMetro_Z 0.0 -12.824 3.97e-09 -3.311
Metro_vs_DEMetro_Z 0.3 -3.353 0.00474 -0.866
Metro_vs_DEMetro_Z 0.5 -10.709 3.97e-08 -2.765
Metro_vs_DEMetro_Z 0.9 -1.707 0.11 -0.441
Metro_vs_DEMetro_Z 0.95 -4.252 0.000804 -1.098
Metro_vs_DEMetro_Z 0.99 1.742 0.104 0.450
HMC_vs_SMC 0.0 -16.030 2.11e-10 -4.139
HMC_vs_SMC 0.3 -17.192 8.27e-11 -4.439
HMC_vs_SMC 0.5 -33.906 7.68e-15 -8.755
HMC_vs_SMC 0.9 -24.313 7.51e-13 -6.278
HMC_vs_SMC 0.95 -27.316 1.52e-13 -7.053
HMC_vs_SMC 0.99 -20.291 8.84e-12 -5.239
Metro_vs_SMC 0.0 -8.412 7.6e-07 -2.172
Metro_vs_SMC 0.3 5.113 0.000158 1.320
Metro_vs_SMC 0.5 -8.033 1.31e-06 -2.074
Metro_vs_SMC 0.9 8.031 1.31e-06 2.074
Metro_vs_SMC 0.95 11.063 2.64e-08 2.856
Metro_vs_SMC 0.99 18.860 2.38e-11 4.870
HMC_vs_DEMetro_Z 0.0 -24.017 8.88e-13 -6.201
HMC_vs_DEMetro_Z 0.3 -20.340 8.56e-12 -5.252
HMC_vs_DEMetro_Z 0.5 -36.891 2.39e-15 -9.525
HMC_vs_DEMetro_Z 0.9 -20.775 6.42e-12 -5.364
HMC_vs_DEMetro_Z 0.95 -33.041 1.1e-14 -8.531
HMC_vs_DEMetro_Z 0.99 -17.154 8.52e-11 -4.429
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.107 0.015 0.001 93.785
HMC 0.3 0.067 0.015 0.002 34.250
HMC 0.5 0.070 0.015 0.002 30.617
HMC 0.9 0.096 0.015 0.006 14.058
HMC 0.95 0.092 0.014 0.005 15.262
HMC 0.99 0.138 0.015 0.006 22.015
SMC 0.0 0.397 0.015 0.001 389.020
SMC 0.3 0.401 0.015 0.002 254.362
SMC 0.5 0.421 0.015 0.002 227.375
SMC 0.9 0.475 0.015 0.006 80.078
SMC 0.95 0.477 0.014 0.005 90.525
SMC 0.99 0.476 0.015 0.006 82.402
Metro 0.0 0.177 0.015 0.001 165.415
Metro 0.3 0.469 0.015 0.002 299.276
Metro 0.5 0.208 0.015 0.002 108.097
Metro 0.9 0.661 0.015 0.006 112.510
Metro 0.95 0.697 0.014 0.005 133.372
Metro 0.99 0.781 0.015 0.006 137.072
DEMetro_Z 0.0 0.500 0.015 0.001 493.416
DEMetro_Z 0.3 0.537 0.015 0.002 344.321
DEMetro_Z 0.5 0.585 0.015 0.002 319.232
DEMetro_Z 0.9 0.726 0.015 0.006 123.920
DEMetro_Z 0.95 0.822 0.014 0.005 157.807
DEMetro_Z 0.99 0.725 0.015 0.006 126.928
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.474 0.159 1.309
HMC 0.3 1.248 0.232 2.760
HMC 0.5 2.672 0.0176 4.480
HMC 0.9 1.267 0.226 7.515
HMC 0.95 3.612 0.00275 9.391
HMC 0.99 2.008 0.0643 10.752
SMC 0.0 13.592 1.13e-12 6.558
SMC 0.3 10.687 4.7e-09 8.393
SMC 0.5 9.270 4.32e-08 7.488
SMC 0.9 8.580 3.33e-07 11.100
SMC 0.95 7.003 5.73e-06 20.865
SMC 0.99 4.068 0.00114 17.632
Metro 0.0 2.039 0.0607 12.655
Metro 0.3 3.356 0.00471 55.085
Metro 0.5 2.533 0.0239 26.665
Metro 0.9 3.320 0.00506 799.812
Metro 0.95 3.845 0.00178 1685.890
Metro 0.99 4.837 0.000264 2751.584
DEMetro_Z 0.0 16.047 2.07e-10 324.736
DEMetro_Z 0.3 6.157 2.49e-05 1930.867
DEMetro_Z 0.5 7.189 4.65e-06 452.600
DEMetro_Z 0.9 5.966 3.45e-05 1694.690
DEMetro_Z 0.95 5.882 3.99e-05 2729.337
DEMetro_Z 0.99 8.586 5.96e-07 1453.311
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -15.919 2.31e-10 -4.110
HMC_vs_DEMetro_Z 0.3 -6.166 2.45e-05 -1.592
HMC_vs_DEMetro_Z 0.5 -7.156 4.89e-06 -1.848
HMC_vs_DEMetro_Z 0.9 -5.904 3.84e-05 -1.524
HMC_vs_DEMetro_Z 0.95 -5.873 4.06e-05 -1.516
HMC_vs_DEMetro_Z 0.99 -8.474 6.97e-07 -2.188
Metro_vs_SMC 0.0 0.976 0.345 0.252
Metro_vs_SMC 0.3 2.862 0.0125 0.739
Metro_vs_SMC 0.5 1.800 0.0935 0.465
Metro_vs_SMC 0.9 3.270 0.00558 0.844
Metro_vs_SMC 0.95 3.797 0.00196 0.980
Metro_vs_SMC 0.99 4.791 0.000287 1.237
Metro_vs_DEMetro_Z 0.0 -15.753 2.66e-10 -4.067
Metro_vs_DEMetro_Z 0.3 -5.900 3.87e-05 -1.523
Metro_vs_DEMetro_Z 0.5 -6.375 1.73e-05 -1.646
Metro_vs_DEMetro_Z 0.9 -1.977 0.068 -0.511
Metro_vs_DEMetro_Z 0.95 -2.452 0.028 -0.633
Metro_vs_DEMetro_Z 0.99 2.212 0.0441 0.571
HMC_vs_Metro 0.0 -1.797 0.0939 -0.464
HMC_vs_Metro 0.3 -3.065 0.0084 -0.791
HMC_vs_Metro 0.5 -1.995 0.0659 -0.515
HMC_vs_Metro 0.9 -3.317 0.00508 -0.857
HMC_vs_Metro 0.95 -3.817 0.00189 -0.986
HMC_vs_Metro 0.99 -4.811 0.000277 -1.242
HMC_vs_SMC 0.0 -5.220 0.00013 -1.348
HMC_vs_SMC 0.3 -2.309 0.0367 -0.596
HMC_vs_SMC 0.5 -1.795 0.0942 -0.464
HMC_vs_SMC 0.9 -0.597 0.56 -0.154
HMC_vs_SMC 0.95 -2.492 0.0258 -0.644
HMC_vs_SMC 0.99 -0.943 0.362 -0.243
DEMetro_Z_vs_SMC 0.0 15.657 2.88e-10 4.043
DEMetro_Z_vs_SMC 0.3 6.126 2.62e-05 1.582
DEMetro_Z_vs_SMC 0.5 7.086 5.46e-06 1.830
DEMetro_Z_vs_SMC 0.9 5.935 3.64e-05 1.532
DEMetro_Z_vs_SMC 0.95 5.827 4.39e-05 1.505
DEMetro_Z_vs_SMC 0.99 8.587 5.95e-07 2.217
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.100 0.067 0.025 1.309
HMC 0.3 0.136 0.075 0.022 2.760
HMC 0.5 0.188 0.069 0.027 4.480
HMC 0.9 0.230 0.041 0.025 7.515
HMC 0.95 0.349 0.053 0.032 9.391
HMC 0.99 0.377 0.049 0.031 10.752
SMC 0.0 0.230 0.067 0.025 6.558
SMC 0.3 0.259 0.075 0.022 8.393
SMC 0.5 0.268 0.069 0.027 7.488
SMC 0.9 0.320 0.041 0.025 11.100
SMC 0.95 0.711 0.053 0.032 20.865
SMC 0.99 0.588 0.049 0.031 17.632
Metro 0.0 0.382 0.067 0.025 12.655
Metro 0.3 1.280 0.075 0.022 55.085
Metro 0.5 0.778 0.069 0.027 26.665
Metro 0.9 20.116 0.041 0.025 799.812
Metro 0.95 53.250 0.053 0.032 1685.890
Metro 0.99 84.081 0.049 0.031 2751.584
DEMetro_Z 0.0 8.128 0.067 0.025 324.736
DEMetro_Z 0.3 42.313 0.075 0.022 1930.867
DEMetro_Z 0.5 12.105 0.069 0.027 452.600
DEMetro_Z 0.9 42.577 0.041 0.025 1694.690
DEMetro_Z 0.95 86.176 0.053 0.032 2729.337
DEMetro_Z 0.99 44.433 0.049 0.031 1453.311
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.611 0.547 0.188
HMC 0.3 0.021 0.983 0.009
HMC 0.5 2.089 0.0487 1.138
HMC 0.9 1.457 0.167 5.698
HMC 0.95 1.124 0.273 0.588
HMC 0.99 0.615 0.545 0.370
SMC 0.0 16.407 1.57e-12 4.583
SMC 0.3 22.652 7e-19 9.465
SMC 0.5 40.525 4.7e-24 18.653
SMC 0.9 13.877 1.39e-09 121.668
SMC 0.95 13.310 2.41e-09 136.479
SMC 0.99 9.916 1.01e-07 72.318
Metro 0.0 1.003 0.332 2.342
Metro 0.3 2.118 0.0523 7.662
Metro 0.5 1.686 0.104 0.759
Metro 0.9 1.975 0.0683 683.362
Metro 0.95 1.674 0.116 1617.562
Metro 0.99 2.256 0.0406 140.650
DEMetro_Z 0.0 10.159 5.85e-08 21.556
DEMetro_Z 0.3 6.409 1.63e-05 356.676
DEMetro_Z 0.5 4.298 0.000725 18.450
DEMetro_Z 0.9 5.677 5.71e-05 301.435
DEMetro_Z 0.95 9.602 1.54e-07 489.585
DEMetro_Z 0.99 7.450 3.03e-06 42.792
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -21.140 5.07e-12 -5.458
HMC_vs_SMC 0.3 -19.169 1.91e-11 -4.949
HMC_vs_SMC 0.5 -24.804 5.71e-13 -6.404
HMC_vs_SMC 0.9 -10.443 5.45e-08 -2.696
HMC_vs_SMC 0.95 -13.199 2.73e-09 -3.408
HMC_vs_SMC 0.99 -9.992 9.44e-08 -2.580
Metro_vs_DEMetro_Z 0.0 -6.488 1.43e-05 -1.675
Metro_vs_DEMetro_Z 0.3 -6.168 2.44e-05 -1.593
Metro_vs_DEMetro_Z 0.5 -4.153 0.000975 -1.072
Metro_vs_DEMetro_Z 0.9 1.169 0.262 0.302
Metro_vs_DEMetro_Z 0.95 1.183 0.256 0.306
Metro_vs_DEMetro_Z 0.99 1.517 0.151 0.392
HMC_vs_Metro 0.0 -0.939 0.363 -0.243
HMC_vs_Metro 0.3 -2.129 0.0515 -0.550
HMC_vs_Metro 0.5 0.781 0.448 0.202
HMC_vs_Metro 0.9 -1.955 0.0709 -0.505
HMC_vs_Metro 0.95 -1.674 0.116 -0.432
HMC_vs_Metro 0.99 -2.247 0.0413 -0.580
HMC_vs_DEMetro_Z 0.0 -9.892 1.07e-07 -2.554
HMC_vs_DEMetro_Z 0.3 -6.415 1.61e-05 -1.656
HMC_vs_DEMetro_Z 0.5 -4.358 0.000656 -1.125
HMC_vs_DEMetro_Z 0.9 -5.538 7.31e-05 -1.430
HMC_vs_DEMetro_Z 0.95 -9.633 1.48e-07 -2.487
HMC_vs_DEMetro_Z 0.99 -7.132 5.08e-06 -1.841
Metro_vs_SMC 0.0 -0.969 0.349 -0.250
Metro_vs_SMC 0.3 -0.510 0.618 -0.132
Metro_vs_SMC 0.5 -32.683 1.28e-14 -8.439
Metro_vs_SMC 0.9 1.635 0.124 0.422
Metro_vs_SMC 0.95 1.539 0.146 0.397
Metro_vs_SMC 0.99 1.059 0.307 0.274
DEMetro_Z_vs_SMC 0.0 8.262 9.39e-07 2.133
DEMetro_Z_vs_SMC 0.3 6.239 2.17e-05 1.611
DEMetro_Z_vs_SMC 0.5 -0.046 0.964 -0.012
DEMetro_Z_vs_SMC 0.9 3.276 0.00552 0.846
DEMetro_Z_vs_SMC 0.95 6.700 1.01e-05 1.730
DEMetro_Z_vs_SMC 0.99 -2.976 0.01 -0.768
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 12.411 8.592 20.294 0.188
HMC 0.3 10.085 9.988 11.248 0.009
HMC 0.5 16.816 8.128 7.632 1.138
HMC 0.9 15.570 3.153 2.179 5.698
HMC 0.95 5.115 3.562 2.643 0.588
HMC 0.99 8.010 5.818 5.919 0.370
SMC 0.0 101.597 8.592 20.294 4.583
SMC 0.3 116.443 9.988 11.248 9.465
SMC 0.5 150.481 8.128 7.632 18.653
SMC 0.9 268.292 3.153 2.179 121.668
SMC 0.95 364.310 3.562 2.643 136.479
SMC 0.99 433.881 5.818 5.919 72.318
Metro 0.0 56.110 8.592 20.294 2.342
Metro 0.3 96.168 9.988 11.248 7.662
Metro 0.5 13.917 8.128 7.632 0.759
Metro 0.9 1492.340 3.153 2.179 683.362
Metro 0.95 4279.162 3.562 2.643 1617.562
Metro 0.99 838.351 5.818 5.919 140.650
DEMetro_Z 0.0 446.049 8.592 20.294 21.556
DEMetro_Z 0.3 4021.757 9.988 11.248 356.676
DEMetro_Z 0.5 148.928 8.128 7.632 18.450
DEMetro_Z 0.9 660.042 3.153 2.179 301.435
DEMetro_Z 0.95 1297.652 3.562 2.643 489.585
DEMetro_Z 0.99 259.111 5.818 5.919 42.792
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.195 0.0455 20.991
HMC 0.3 3.067 0.00832 17.501
HMC 0.5 3.143 0.00717 18.861
HMC 0.9 2.646 0.0192 39.273
HMC 0.95 5.616 6.11e-05 19.918
HMC 0.99 2.622 0.0201 23.930
SMC 0.0 82.027 1.94e-20 237.394
SMC 0.3 53.470 1.24e-17 337.419
SMC 0.5 104.318 8.55e-22 408.964
SMC 0.9 34.676 5.61e-15 1117.665
SMC 0.95 28.749 7.47e-14 679.383
SMC 0.99 20.506 7.64e-12 633.060
Metro 0.0 2.304 0.0371 37.042
Metro 0.3 3.150 0.00709 155.629
Metro 0.5 2.968 0.0102 46.828
Metro 0.9 3.344 0.00482 1769.951
Metro 0.95 4.208 0.000877 2637.424
Metro 0.99 4.838 0.000263 3197.555
DEMetro_Z 0.0 18.648 2.76e-11 545.160
DEMetro_Z 0.3 10.349 6.1e-08 2615.807
DEMetro_Z 0.5 9.049 3.17e-07 607.349
DEMetro_Z 0.9 7.673 2.22e-06 4051.386
DEMetro_Z 0.95 6.903 7.29e-06 4053.387
DEMetro_Z 0.99 9.526 1.7e-07 1762.899
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -15.417 3.54e-10 -3.981
Metro_vs_DEMetro_Z 0.3 -9.080 3.05e-07 -2.344
Metro_vs_DEMetro_Z 0.5 -7.910 1.56e-06 -2.042
Metro_vs_DEMetro_Z 0.9 -2.612 0.0205 -0.674
Metro_vs_DEMetro_Z 0.95 -2.693 0.0175 -0.695
Metro_vs_DEMetro_Z 0.99 2.121 0.0522 0.548
DEMetro_Z_vs_SMC 0.0 10.865 3.31e-08 2.805
DEMetro_Z_vs_SMC 0.3 8.947 3.64e-07 2.310
DEMetro_Z_vs_SMC 0.5 2.910 0.0114 0.751
DEMetro_Z_vs_SMC 0.9 5.497 7.87e-05 1.419
DEMetro_Z_vs_SMC 0.95 5.756 4.97e-05 1.486
DEMetro_Z_vs_SMC 0.99 6.199 2.32e-05 1.601
HMC_vs_DEMetro_Z 0.0 -15.583 3.07e-10 -4.024
HMC_vs_DEMetro_Z 0.3 -10.398 5.75e-08 -2.685
HMC_vs_DEMetro_Z 0.5 -8.640 5.53e-07 -2.231
HMC_vs_DEMetro_Z 0.9 -7.516 2.81e-06 -1.941
HMC_vs_DEMetro_Z 0.95 -6.879 7.58e-06 -1.776
HMC_vs_DEMetro_Z 0.99 -9.249 2.44e-07 -2.388
HMC_vs_Metro 0.0 -0.838 0.416 -0.216
HMC_vs_Metro 0.3 -2.675 0.0181 -0.691
HMC_vs_Metro 0.5 -1.558 0.142 -0.402
HMC_vs_Metro 0.9 -3.287 0.0054 -0.849
HMC_vs_Metro 0.95 -4.169 0.000945 -1.077
HMC_vs_Metro 0.99 -4.787 0.00029 -1.236
HMC_vs_SMC 0.0 -20.673 6.86e-12 -5.338
HMC_vs_SMC 0.3 -33.902 7.7e-15 -8.754
HMC_vs_SMC 0.5 -53.693 1.29e-17 -13.864
HMC_vs_SMC 0.9 -36.207 3.1e-15 -9.349
HMC_vs_SMC 0.95 -25.909 3.14e-13 -6.690
HMC_vs_SMC 0.99 -20.490 7.74e-12 -5.290
Metro_vs_SMC 0.0 -12.303 6.78e-09 -3.177
Metro_vs_SMC 0.3 -3.827 0.00185 -0.988
Metro_vs_SMC 0.5 -25.076 4.92e-13 -6.474
Metro_vs_SMC 0.9 1.250 0.232 0.323
Metro_vs_SMC 0.95 3.166 0.00687 0.818
Metro_vs_SMC 0.99 3.839 0.0018 0.991
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.702 0.114 0.028 20.991
HMC 0.3 0.490 0.121 0.021 17.501
HMC 0.5 0.505 0.118 0.021 18.861
HMC 0.9 0.481 0.094 0.010 39.273
HMC 0.95 0.462 0.094 0.018 19.918
HMC 0.99 0.609 0.095 0.021 23.930
SMC 0.0 6.761 0.114 0.028 237.394
SMC 0.3 7.249 0.121 0.021 337.419
SMC 0.5 8.513 0.118 0.021 408.964
SMC 0.9 11.115 0.094 0.010 1117.665
SMC 0.95 12.659 0.094 0.018 679.383
SMC 0.99 13.688 0.095 0.021 633.060
Metro 0.0 1.151 0.114 0.028 37.042
Metro 0.3 3.409 0.121 0.021 155.629
Metro 0.5 1.079 0.118 0.021 46.828
Metro 0.9 17.547 0.094 0.010 1769.951
Metro 0.95 48.874 0.094 0.018 2637.424
Metro 0.99 68.751 0.095 0.021 3197.555
DEMetro_Z 0.0 15.379 0.114 0.028 545.160
DEMetro_Z 0.3 55.383 0.121 0.021 2615.807
DEMetro_Z 0.5 12.585 0.118 0.021 607.349
DEMetro_Z 0.9 40.044 0.094 0.010 4051.386
DEMetro_Z 0.95 75.062 0.094 0.018 4053.387
DEMetro_Z 0.99 37.947 0.095 0.021 1762.899
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.329 0.0353 71.246
HMC 0.3 2.112 0.0531 61.719
HMC 0.5 2.149 0.0496 37.974
HMC 0.9 1.956 0.0706 19.936
HMC 0.95 6.659 9.65e-06 16.272
HMC 0.99 4.332 0.000682 21.613
SMC 0.0 125.642 4.98e-23 391.026
SMC 0.3 84.272 1.44e-20 264.216
SMC 0.5 91.135 3.84e-21 240.655
SMC 0.9 80.938 5.27e-22 87.248
SMC 0.95 53.315 4.67e-18 102.814
SMC 0.99 41.923 2.09e-16 99.144
Metro 0.0 6.573 1.24e-05 130.717
Metro 0.3 6.330 1.86e-05 189.040
Metro 0.5 4.960 0.000209 103.314
Metro 0.9 16.432 1.45e-10 113.267
Metro 0.95 39.244 8.63e-16 184.738
Metro 0.99 60.284 1.68e-18 192.413
DEMetro_Z 0.0 43.982 2.03e-16 535.171
DEMetro_Z 0.3 23.205 1.41e-12 406.742
DEMetro_Z 0.5 20.041 1.04e-11 375.484
DEMetro_Z 0.9 17.457 6.52e-11 141.012
DEMetro_Z 0.95 15.789 2.54e-10 170.855
DEMetro_Z 0.99 29.642 4.49e-14 170.372
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 11.274 2.07e-08 2.911
DEMetro_Z_vs_SMC 0.3 7.460 3.06e-06 1.926
DEMetro_Z_vs_SMC 0.5 6.711 9.92e-06 1.733
DEMetro_Z_vs_SMC 0.9 6.432 1.57e-05 1.661
DEMetro_Z_vs_SMC 0.95 6.253 2.12e-05 1.614
DEMetro_Z_vs_SMC 0.99 11.345 1.92e-08 2.929
HMC_vs_Metro 0.0 -1.534 0.147 -0.396
HMC_vs_Metro 0.3 -2.574 0.0221 -0.665
HMC_vs_Metro 0.5 -2.242 0.0417 -0.579
HMC_vs_Metro 0.9 -7.932 1.51e-06 -2.048
HMC_vs_Metro 0.95 -31.855 1.82e-14 -8.225
HMC_vs_Metro 0.99 -27.875 1.15e-13 -7.197
Metro_vs_DEMetro_Z 0.0 -19.480 1.54e-11 -5.030
Metro_vs_DEMetro_Z 0.3 -5.738 5.13e-05 -1.482
Metro_vs_DEMetro_Z 0.5 -9.118 2.89e-07 -2.354
Metro_vs_DEMetro_Z 0.9 -2.959 0.0104 -0.764
Metro_vs_DEMetro_Z 0.95 1.085 0.296 0.280
Metro_vs_DEMetro_Z 0.99 3.010 0.00937 0.777
HMC_vs_SMC 0.0 -10.171 7.57e-08 -2.626
HMC_vs_SMC 0.3 -6.807 8.51e-06 -1.757
HMC_vs_SMC 0.5 -11.634 1.39e-08 -3.004
HMC_vs_SMC 0.9 -6.841 8.05e-06 -1.766
HMC_vs_SMC 0.95 -22.655 1.97e-12 -5.849
HMC_vs_SMC 0.99 -16.122 1.95e-10 -4.163
Metro_vs_SMC 0.0 -12.799 4.07e-09 -3.305
Metro_vs_SMC 0.3 -2.548 0.0232 -0.658
Metro_vs_SMC 0.5 -6.549 1.29e-05 -1.691
Metro_vs_SMC 0.9 3.722 0.00227 0.961
Metro_vs_SMC 0.95 17.006 9.57e-11 4.391
Metro_vs_SMC 0.99 21.514 3.99e-12 5.555
HMC_vs_DEMetro_Z 0.0 -16.621 1.3e-10 -4.291
HMC_vs_DEMetro_Z 0.3 -10.244 6.93e-08 -2.645
HMC_vs_DEMetro_Z 0.5 -14.463 8.23e-10 -3.734
HMC_vs_DEMetro_Z 0.9 -8.946 3.64e-07 -2.310
HMC_vs_DEMetro_Z 0.95 -13.690 1.69e-09 -3.535
HMC_vs_DEMetro_Z 0.99 -19.400 1.62e-11 -5.009
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.085 0.015 0.001 71.246
HMC 0.3 0.108 0.015 0.002 61.719
HMC 0.5 0.083 0.015 0.002 37.974
HMC 0.9 0.130 0.015 0.006 19.936
HMC 0.95 0.097 0.014 0.005 16.272
HMC 0.99 0.136 0.015 0.006 21.613
SMC 0.0 0.399 0.015 0.001 391.026
SMC 0.3 0.416 0.015 0.002 264.216
SMC 0.5 0.445 0.015 0.002 240.655
SMC 0.9 0.516 0.015 0.006 87.248
SMC 0.95 0.540 0.014 0.005 102.814
SMC 0.99 0.569 0.015 0.006 99.144
Metro 0.0 0.143 0.015 0.001 130.717
Metro 0.3 0.302 0.015 0.002 189.040
Metro 0.5 0.199 0.015 0.002 103.314
Metro 0.9 0.665 0.015 0.006 113.267
Metro 0.95 0.960 0.014 0.005 184.738
Metro 0.99 1.091 0.015 0.006 192.413
DEMetro_Z 0.0 0.541 0.015 0.001 535.171
DEMetro_Z 0.3 0.632 0.015 0.002 406.742
DEMetro_Z 0.5 0.685 0.015 0.002 375.484
DEMetro_Z 0.9 0.824 0.015 0.006 141.012
DEMetro_Z 0.95 0.889 0.014 0.005 170.855
DEMetro_Z 0.99 0.968 0.015 0.006 170.372
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
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0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
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Vary_Correlation_with_Dim_and_MM (Mixture, correlation, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.814 0.000275 70.881
HMC 0.3 5.131 0.00015 24.324
HMC 0.5 4.988 0.000196 27.121
HMC 0.9 7.926 7.96e-07 9.241
HMC 0.95 4.400 0.000551 7.980
HMC 0.99 5.755 4.5e-05 12.978
SMC 0.0 1.323 0.201 0.836
SMC 0.3 -0.731 0.471 -0.279
SMC 0.5 -0.504 0.618 -0.172
SMC 0.9 0.733 0.47 0.253
SMC 0.95 0.019 0.985 0.006
SMC 0.99 0.444 0.661 0.183
Metro 0.0 5.665 5.71e-05 27.768
Metro 0.3 5.645 5.68e-05 15.921
Metro 0.5 6.621 1.03e-05 16.230
Metro 0.9 4.561 0.000441 34.929
Metro 0.95 6.028 3.03e-05 29.984
Metro 0.99 6.324 1.86e-05 56.963
DEMetro_Z 0.0 30.841 2.85e-14 2097.404
DEMetro_Z 0.3 25.034 5.02e-13 898.888
DEMetro_Z 0.5 32.142 1.6e-14 1057.912
DEMetro_Z 0.9 39.601 8.82e-16 673.833
DEMetro_Z 0.95 27.294 1.51e-13 363.484
DEMetro_Z 0.99 27.364 1.47e-13 501.370
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -31.761 1.9e-14 -8.201
HMC_vs_DEMetro_Z 0.3 -23.936 9.3e-13 -6.180
HMC_vs_DEMetro_Z 0.5 -31.529 2.1e-14 -8.141
HMC_vs_DEMetro_Z 0.9 -39.016 1.1e-15 -10.074
HMC_vs_DEMetro_Z 0.95 -26.196 2.7e-13 -6.764
HMC_vs_DEMetro_Z 0.99 -25.872 3.2e-13 -6.680
Metro_vs_SMC 0.0 5.269 0.000119 1.360
Metro_vs_SMC 0.3 5.875 4.04e-05 1.517
Metro_vs_SMC 0.5 6.665 1.07e-05 1.721
Metro_vs_SMC 0.9 4.526 0.000475 1.169
Metro_vs_SMC 0.95 6.096 2.76e-05 1.574
Metro_vs_SMC 0.99 6.346 1.81e-05 1.638
Metro_vs_DEMetro_Z 0.0 -30.277 3.67e-14 -7.817
Metro_vs_DEMetro_Z 0.3 -24.388 7.2e-13 -6.297
Metro_vs_DEMetro_Z 0.5 -31.692 1.96e-14 -8.183
Metro_vs_DEMetro_Z 0.9 -40.679 6.15e-16 -10.503
Metro_vs_DEMetro_Z 0.95 -24.398 7.16e-13 -6.299
Metro_vs_DEMetro_Z 0.99 -19.344 1.69e-11 -4.995
HMC_vs_Metro 0.0 2.698 0.0173 0.696
HMC_vs_Metro 0.3 1.290 0.218 0.333
HMC_vs_Metro 0.5 1.636 0.124 0.422
HMC_vs_Metro 0.9 -3.111 0.00766 -0.803
HMC_vs_Metro 0.95 -4.007 0.0013 -1.035
HMC_vs_Metro 0.99 -4.737 0.000318 -1.223
HMC_vs_SMC 0.0 4.784 0.000291 1.235
HMC_vs_SMC 0.3 5.187 0.000138 1.339
HMC_vs_SMC 0.5 5.060 0.000174 1.306
HMC_vs_SMC 0.9 8.181 1.05e-06 2.112
HMC_vs_SMC 0.95 4.713 0.000333 1.217
HMC_vs_SMC 0.99 5.618 6.34e-05 1.451
DEMetro_Z_vs_SMC 0.0 30.842 2.85e-14 7.963
DEMetro_Z_vs_SMC 0.3 25.048 4.99e-13 6.467
DEMetro_Z_vs_SMC 0.5 32.161 1.6e-14 8.304
DEMetro_Z_vs_SMC 0.9 39.602 8.93e-16 10.225
DEMetro_Z_vs_SMC 0.95 27.279 1.55e-13 7.043
DEMetro_Z_vs_SMC 0.99 27.327 1.51e-13 7.056
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.256 0.025 0.003 70.881
HMC 0.3 0.202 0.028 0.007 24.324
HMC 0.5 0.210 0.023 0.007 27.121
HMC 0.9 0.110 0.021 0.010 9.241
HMC 0.95 0.163 0.022 0.018 7.980
HMC 0.99 0.161 0.015 0.011 12.978
SMC 0.0 0.028 0.025 0.003 0.836
SMC 0.3 0.026 0.028 0.007 -0.279
SMC 0.5 0.022 0.023 0.007 -0.172
SMC 0.9 0.024 0.021 0.010 0.253
SMC 0.95 0.022 0.022 0.018 0.006
SMC 0.99 0.017 0.015 0.011 0.183
Metro 0.0 0.116 0.025 0.003 27.768
Metro 0.3 0.142 0.028 0.007 15.921
Metro 0.5 0.135 0.023 0.007 16.230
Metro 0.9 0.356 0.021 0.010 34.929
Metro 0.95 0.550 0.022 0.018 29.984
Metro 0.99 0.654 0.015 0.011 56.963
DEMetro_Z 0.0 6.845 0.025 0.003 2097.404
DEMetro_Z 0.3 6.450 0.028 0.007 898.888
DEMetro_Z 0.5 7.307 0.023 0.007 1057.912
DEMetro_Z 0.9 6.478 0.021 0.010 673.833
DEMetro_Z 0.95 6.423 0.022 0.018 363.484
DEMetro_Z 0.99 5.635 0.015 0.011 501.370
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.600 0.021 31.358
HMC 0.3 3.378 0.00449 26.345
HMC 0.5 3.355 0.0047 26.461
HMC 0.9 4.191 0.000868 10.474
HMC 0.95 4.133 0.000956 8.698
HMC 0.99 4.899 0.000162 4.933
SMC 0.0 2.163 0.0403 0.973
SMC 0.3 1.745 0.0964 1.062
SMC 0.5 1.820 0.0795 0.633
SMC 0.9 2.304 0.0309 1.190
SMC 0.95 -0.452 0.655 -0.188
SMC 0.99 -1.154 0.26 -0.357
Metro 0.0 3.182 0.00612 4.103
Metro 0.3 3.572 0.00302 13.000
Metro 0.5 5.724 4.31e-05 9.249
Metro 0.9 5.001 0.000192 28.343
Metro 0.95 3.501 0.00353 56.266
Metro 0.99 4.555 0.000449 122.944
DEMetro_Z 0.0 25.115 4.81e-13 10783.756
DEMetro_Z 0.3 22.326 2.41e-12 16880.622
DEMetro_Z 0.5 33.754 8.18e-15 13831.434
DEMetro_Z 0.9 26.794 1.98e-13 14912.195
DEMetro_Z 0.95 34.074 7.18e-15 11327.388
DEMetro_Z 0.99 23.428 1.25e-12 7228.223
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 2.512 0.0249 0.648
HMC_vs_SMC 0.3 3.295 0.00532 0.851
HMC_vs_SMC 0.5 3.277 0.00551 0.846
HMC_vs_SMC 0.9 4.012 0.00129 1.036
HMC_vs_SMC 0.95 4.015 0.00128 1.037
HMC_vs_SMC 0.99 5.377 9.75e-05 1.388
Metro_vs_DEMetro_Z 0.0 -25.100 4.85e-13 -6.481
Metro_vs_DEMetro_Z 0.3 -22.337 2.39e-12 -5.767
Metro_vs_DEMetro_Z 0.5 -33.706 8.34e-15 -8.703
Metro_vs_DEMetro_Z 0.9 -26.682 2.1e-13 -6.889
Metro_vs_DEMetro_Z 0.95 -34.158 6.94e-15 -8.820
Metro_vs_DEMetro_Z 0.99 -23.377 1.29e-12 -6.036
HMC_vs_Metro 0.0 2.241 0.0418 0.579
HMC_vs_Metro 0.3 1.396 0.184 0.361
HMC_vs_Metro 0.5 1.978 0.0679 0.511
HMC_vs_Metro 0.9 -2.640 0.0194 -0.682
HMC_vs_Metro 0.95 -2.937 0.0108 -0.758
HMC_vs_Metro 0.99 -4.407 0.000596 -1.138
HMC_vs_DEMetro_Z 0.0 -25.141 4.74e-13 -6.491
HMC_vs_DEMetro_Z 0.3 -22.220 2.57e-12 -5.737
HMC_vs_DEMetro_Z 0.5 -33.689 8.4e-15 -8.699
HMC_vs_DEMetro_Z 0.9 -26.780 1.99e-13 -6.915
HMC_vs_DEMetro_Z 0.95 -34.035 7.29e-15 -8.788
HMC_vs_DEMetro_Z 0.99 -23.411 1.26e-12 -6.045
Metro_vs_SMC 0.0 2.573 0.0221 0.664
Metro_vs_SMC 0.3 3.234 0.006 0.835
Metro_vs_SMC 0.5 5.570 6.9e-05 1.438
Metro_vs_SMC 0.9 4.884 0.000241 1.261
Metro_vs_SMC 0.95 3.565 0.00311 0.920
Metro_vs_SMC 0.99 4.556 0.000449 1.176
DEMetro_Z_vs_SMC 0.0 25.121 4.8e-13 6.486
DEMetro_Z_vs_SMC 0.3 22.321 2.42e-12 5.763
DEMetro_Z_vs_SMC 0.5 33.756 8.17e-15 8.716
DEMetro_Z_vs_SMC 0.9 26.793 1.98e-13 6.918
DEMetro_Z_vs_SMC 0.95 34.080 7.16e-15 8.799
DEMetro_Z_vs_SMC 0.99 23.429 1.25e-12 6.049
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.546 0.043 0.016 31.358
HMC 0.3 0.312 0.039 0.010 26.345
HMC 0.5 0.381 0.036 0.013 26.461
HMC 0.9 0.151 0.026 0.012 10.474
HMC 0.95 0.145 0.028 0.013 8.698
HMC 0.99 0.128 0.024 0.021 4.933
SMC 0.0 0.059 0.043 0.016 0.973
SMC 0.3 0.050 0.039 0.010 1.062
SMC 0.5 0.044 0.036 0.013 0.633
SMC 0.9 0.041 0.026 0.012 1.190
SMC 0.95 0.026 0.028 0.013 -0.188
SMC 0.99 0.017 0.024 0.021 -0.357
Metro 0.0 0.109 0.043 0.016 4.103
Metro 0.3 0.174 0.039 0.010 13.000
Metro 0.5 0.156 0.036 0.013 9.249
Metro 0.9 0.365 0.026 0.012 28.343
Metro 0.95 0.781 0.028 0.013 56.266
Metro 0.99 2.593 0.024 0.021 122.944
DEMetro_Z 0.0 173.130 0.043 0.016 10783.756
DEMetro_Z 0.3 174.677 0.039 0.010 16880.622
DEMetro_Z 0.5 180.498 0.036 0.013 13831.434
DEMetro_Z 0.9 178.222 0.026 0.012 14912.195
DEMetro_Z 0.95 151.667 0.028 0.013 11327.388
DEMetro_Z 0.99 151.049 0.024 0.021 7228.223
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.671 0.00036 94.992
HMC 0.3 5.036 0.000179 25.765
HMC 0.5 5.065 0.000171 34.700
HMC 0.9 8.190 7.98e-07 15.261
HMC 0.95 4.845 0.000244 11.777
HMC 0.99 6.215 2.07e-05 16.297
SMC 0.0 2.174 0.0434 1.593
SMC 0.3 -0.324 0.748 -0.109
SMC 0.5 -0.188 0.852 -0.062
SMC 0.9 0.727 0.473 0.259
SMC 0.95 -0.073 0.942 -0.024
SMC 0.99 -0.205 0.839 -0.073
Metro 0.0 5.346 0.000102 36.439
Metro 0.3 5.802 4.34e-05 17.850
Metro 0.5 7.428 2.94e-06 22.257
Metro 0.9 7.043 5.78e-06 62.122
Metro 0.95 7.231 4.28e-06 49.521
Metro 0.99 9.154 2.74e-07 116.026
DEMetro_Z 0.0 40.010 7.74e-16 5573.215
DEMetro_Z 0.3 53.034 1.53e-17 2020.117
DEMetro_Z 0.5 76.366 9.44e-20 2596.765
DEMetro_Z 0.9 61.179 2.09e-18 2029.778
DEMetro_Z 0.95 72.430 1.94e-19 1000.680
DEMetro_Z 0.99 48.794 4.87e-17 1262.941
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -39.341 9.78e-16 -10.158
Metro_vs_DEMetro_Z 0.3 -53.452 1.38e-17 -13.801
Metro_vs_DEMetro_Z 0.5 -75.130 1.19e-19 -19.398
Metro_vs_DEMetro_Z 0.9 -61.128 2.12e-18 -15.783
Metro_vs_DEMetro_Z 0.95 -63.188 1.33e-18 -16.315
Metro_vs_DEMetro_Z 0.99 -36.162 3.15e-15 -9.337
DEMetro_Z_vs_SMC 0.0 40.045 7.65e-16 10.339
DEMetro_Z_vs_SMC 0.3 53.053 1.53e-17 13.698
DEMetro_Z_vs_SMC 0.5 76.260 9.66e-20 19.690
DEMetro_Z_vs_SMC 0.9 61.135 2.12e-18 15.785
DEMetro_Z_vs_SMC 0.95 72.354 2.01e-19 18.682
DEMetro_Z_vs_SMC 0.99 48.893 4.76e-17 12.624
HMC_vs_DEMetro_Z 0.0 -40.714 6.08e-16 -10.512
HMC_vs_DEMetro_Z 0.3 -50.031 3.46e-17 -12.918
HMC_vs_DEMetro_Z 0.5 -74.545 1.33e-19 -19.247
HMC_vs_DEMetro_Z 0.9 -61.429 1.98e-18 -15.861
HMC_vs_DEMetro_Z 0.95 -70.010 3.19e-19 -18.076
HMC_vs_DEMetro_Z 0.99 -46.912 8.47e-17 -12.113
HMC_vs_Metro 0.0 2.649 0.0191 0.684
HMC_vs_Metro 0.3 1.128 0.278 0.291
HMC_vs_Metro 0.5 1.481 0.161 0.382
HMC_vs_Metro 0.9 -4.770 0.000299 -1.232
HMC_vs_Metro 0.95 -5.015 0.000189 -1.295
HMC_vs_Metro 0.99 -8.507 6.65e-07 -2.197
HMC_vs_SMC 0.0 4.622 0.000396 1.193
HMC_vs_SMC 0.3 5.057 0.000175 1.306
HMC_vs_SMC 0.5 5.112 0.000158 1.320
HMC_vs_SMC 0.9 8.416 7.55e-07 2.173
HMC_vs_SMC 0.95 5.097 0.000163 1.316
HMC_vs_SMC 0.99 6.080 2.84e-05 1.570
Metro_vs_SMC 0.0 4.928 0.000222 1.272
Metro_vs_SMC 0.3 5.967 3.45e-05 1.541
Metro_vs_SMC 0.5 7.552 2.66e-06 1.950
Metro_vs_SMC 0.9 6.971 6.54e-06 1.800
Metro_vs_SMC 0.95 7.298 3.92e-06 1.884
Metro_vs_SMC 0.99 9.108 2.93e-07 2.352
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.206 0.033 0.002 94.992
HMC 0.3 0.164 0.034 0.005 25.765
HMC 0.5 0.171 0.030 0.004 34.700
HMC 0.9 0.105 0.026 0.005 15.261
HMC 0.95 0.142 0.027 0.010 11.777
HMC 0.99 0.147 0.024 0.008 16.297
SMC 0.0 0.036 0.033 0.002 1.593
SMC 0.3 0.033 0.034 0.005 -0.109
SMC 0.5 0.030 0.030 0.004 -0.062
SMC 0.9 0.028 0.026 0.005 0.259
SMC 0.95 0.027 0.027 0.010 -0.024
SMC 0.99 0.023 0.024 0.008 -0.073
Metro 0.0 0.099 0.033 0.002 36.439
Metro 0.3 0.124 0.034 0.005 17.850
Metro 0.5 0.121 0.030 0.004 22.257
Metro 0.9 0.347 0.026 0.005 62.122
Metro 0.95 0.512 0.027 0.010 49.521
Metro 0.99 0.899 0.024 0.008 116.026
DEMetro_Z 0.0 10.214 0.033 0.002 5573.215
DEMetro_Z 0.3 10.214 0.034 0.005 2020.117
DEMetro_Z 0.5 10.595 0.030 0.004 2596.765
DEMetro_Z 0.9 10.519 0.026 0.005 2029.778
DEMetro_Z 0.95 9.831 0.027 0.010 1000.680
DEMetro_Z 0.99 9.552 0.024 0.008 1262.941
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.881 0.000242 74.771
HMC 0.3 5.136 0.000149 27.462
HMC 0.5 4.891 0.000237 44.755
HMC 0.9 8.008 1.06e-06 15.365
HMC 0.95 6.445 1.29e-05 12.223
HMC 0.99 6.402 1.37e-05 11.818
SMC 0.0 2.051 0.0536 1.234
SMC 0.3 -0.394 0.697 -0.153
SMC 0.5 -0.269 0.79 -0.093
SMC 0.9 0.758 0.455 0.264
SMC 0.95 0.033 0.974 0.012
SMC 0.99 -0.326 0.747 -0.107
Metro 0.0 5.763 4.81e-05 29.047
Metro 0.3 5.701 5.2e-05 18.077
Metro 0.5 8.671 4.74e-07 25.893
Metro 0.9 8.942 3.55e-07 50.295
Metro 0.95 8.689 4.97e-07 43.823
Metro 0.99 11.187 2.22e-08 73.974
DEMetro_Z 0.0 71.624 2.01e-19 409.272
DEMetro_Z 0.3 54.660 7.1e-18 188.329
DEMetro_Z 0.5 58.551 3.17e-18 272.601
DEMetro_Z 0.9 60.121 1.19e-18 139.309
DEMetro_Z 0.95 74.402 3.14e-21 84.842
DEMetro_Z 0.99 65.812 6.16e-20 89.270
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 69.445 3.57e-19 17.931
DEMetro_Z_vs_SMC 0.3 55.184 8.82e-18 14.248
DEMetro_Z_vs_SMC 0.5 57.930 4.48e-18 14.957
DEMetro_Z_vs_SMC 0.9 59.981 2.76e-18 15.487
DEMetro_Z_vs_SMC 0.95 70.423 2.94e-19 18.183
DEMetro_Z_vs_SMC 0.99 62.444 1.57e-18 16.123
HMC_vs_Metro 0.0 2.750 0.0156 0.710
HMC_vs_Metro 0.3 1.274 0.223 0.329
HMC_vs_Metro 0.5 1.761 0.1 0.455
HMC_vs_Metro 0.9 -5.392 9.5e-05 -1.392
HMC_vs_Metro 0.95 -5.348 0.000103 -1.381
HMC_vs_Metro 0.99 -9.764 1.26e-07 -2.521
Metro_vs_DEMetro_Z 0.0 -70.794 2.73e-19 -18.279
Metro_vs_DEMetro_Z 0.3 -38.226 1.46e-15 -9.870
Metro_vs_DEMetro_Z 0.5 -41.491 4.67e-16 -10.713
Metro_vs_DEMetro_Z 0.9 -16.902 1.04e-10 -4.364
Metro_vs_DEMetro_Z 0.95 -8.100 1.18e-06 -2.091
Metro_vs_DEMetro_Z 0.99 -2.204 0.0448 -0.569
HMC_vs_SMC 0.0 4.837 0.000264 1.249
HMC_vs_SMC 0.3 5.164 0.000144 1.333
HMC_vs_SMC 0.5 4.954 0.000212 1.279
HMC_vs_SMC 0.9 8.333 8.5e-07 2.151
HMC_vs_SMC 0.95 6.740 9.48e-06 1.740
HMC_vs_SMC 0.99 6.286 2e-05 1.623
Metro_vs_SMC 0.0 5.348 0.000103 1.381
Metro_vs_SMC 0.3 5.901 3.86e-05 1.524
Metro_vs_SMC 0.5 8.708 5.04e-07 2.248
Metro_vs_SMC 0.9 8.914 3.81e-07 2.301
Metro_vs_SMC 0.95 8.854 4.12e-07 2.286
Metro_vs_SMC 0.99 11.103 2.52e-08 2.867
HMC_vs_DEMetro_Z 0.0 -23.933 9.31e-13 -6.180
HMC_vs_DEMetro_Z 0.3 -25.265 4.43e-13 -6.524
HMC_vs_DEMetro_Z 0.5 -23.805 1e-12 -6.147
HMC_vs_DEMetro_Z 0.9 -41.720 4.33e-16 -10.772
HMC_vs_DEMetro_Z 0.95 -30.966 2.69e-14 -7.995
HMC_vs_DEMetro_Z 0.99 -33.641 8.57e-15 -8.686
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.116 0.013 0.001 74.771
HMC 0.3 0.096 0.015 0.003 27.462
HMC 0.5 0.109 0.013 0.002 44.755
HMC 0.9 0.074 0.014 0.004 15.365
HMC 0.95 0.095 0.016 0.006 12.223
HMC 0.99 0.087 0.014 0.006 11.818
SMC 0.0 0.015 0.013 0.001 1.234
SMC 0.3 0.014 0.015 0.003 -0.153
SMC 0.5 0.013 0.013 0.002 -0.093
SMC 0.9 0.015 0.014 0.004 0.264
SMC 0.95 0.016 0.016 0.006 0.012
SMC 0.99 0.014 0.014 0.006 -0.107
Metro 0.0 0.053 0.013 0.001 29.047
Metro 0.3 0.068 0.015 0.003 18.077
Metro 0.5 0.069 0.013 0.002 25.893
Metro 0.9 0.209 0.014 0.004 50.295
Metro 0.95 0.300 0.016 0.006 43.823
Metro 0.99 0.469 0.014 0.006 73.974
DEMetro_Z 0.0 0.575 0.013 0.001 409.272
DEMetro_Z 0.3 0.575 0.015 0.003 188.329
DEMetro_Z 0.5 0.594 0.013 0.002 272.601
DEMetro_Z 0.9 0.555 0.014 0.004 139.309
DEMetro_Z 0.95 0.566 0.016 0.006 84.842
DEMetro_Z 0.99 0.563 0.014 0.006 89.270
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.453 1.51e-05 109.645
HMC 0.3 7.729 2.01e-06 54.207
HMC 0.5 9.750 1.23e-07 57.288
HMC 0.9 10.291 4.73e-08 20.145
HMC 0.95 7.093 2.81e-06 7.605
HMC 0.99 4.834 0.000247 11.306
SMC 0.0 0.650 0.523 0.410
SMC 0.3 -1.005 0.324 -0.316
SMC 0.5 0.118 0.907 0.040
SMC 0.9 0.186 0.854 0.085
SMC 0.95 -0.891 0.381 -0.290
SMC 0.99 0.465 0.646 0.184
Metro 0.0 4.382 0.000611 15.884
Metro 0.3 5.364 9.43e-05 15.194
Metro 0.5 5.374 9.42e-05 18.238
Metro 0.9 6.368 1.72e-05 44.321
Metro 0.95 5.242 0.000123 31.889
Metro 0.99 4.084 0.00112 109.056
DEMetro_Z 0.0 17.455 6.74e-11 3009.788
DEMetro_Z 0.3 22.596 2.04e-12 1711.845
DEMetro_Z 0.5 30.874 2.8e-14 1736.894
DEMetro_Z 0.9 33.123 1.06e-14 1237.780
DEMetro_Z 0.95 44.239 1.88e-16 645.889
DEMetro_Z 0.99 28.452 8.64e-14 921.289
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -16.449 1.49e-10 -4.247
HMC_vs_DEMetro_Z 0.3 -21.481 4.07e-12 -5.546
HMC_vs_DEMetro_Z 0.5 -29.828 4.52e-14 -7.701
HMC_vs_DEMetro_Z 0.9 -32.702 1.27e-14 -8.444
HMC_vs_DEMetro_Z 0.95 -44.127 1.98e-16 -11.394
HMC_vs_DEMetro_Z 0.99 -27.509 1.38e-13 -7.103
Metro_vs_SMC 0.0 3.918 0.00155 1.012
Metro_vs_SMC 0.3 5.340 0.000104 1.379
Metro_vs_SMC 0.5 5.312 0.00011 1.371
Metro_vs_SMC 0.9 6.294 1.98e-05 1.625
Metro_vs_SMC 0.95 5.225 0.000129 1.349
Metro_vs_SMC 0.99 4.098 0.00109 1.058
Metro_vs_DEMetro_Z 0.0 -17.344 7.35e-11 -4.478
Metro_vs_DEMetro_Z 0.3 -22.727 1.89e-12 -5.868
Metro_vs_DEMetro_Z 0.5 -30.835 2.86e-14 -7.962
Metro_vs_DEMetro_Z 0.9 -30.969 2.69e-14 -7.996
Metro_vs_DEMetro_Z 0.95 -43.711 2.26e-16 -11.286
Metro_vs_DEMetro_Z 0.99 -21.036 5.42e-12 -5.431
HMC_vs_Metro 0.0 5.928 3.69e-05 1.531
HMC_vs_Metro 0.3 5.422 8.99e-05 1.400
HMC_vs_Metro 0.5 6.898 7.35e-06 1.781
HMC_vs_Metro 0.9 -3.539 0.00327 -0.914
HMC_vs_Metro 0.95 -3.677 0.00249 -0.949
HMC_vs_Metro 0.99 -3.651 0.00262 -0.943
HMC_vs_SMC 0.0 6.351 1.79e-05 1.640
HMC_vs_SMC 0.3 7.720 2.07e-06 1.993
HMC_vs_SMC 0.5 9.707 1.35e-07 2.506
HMC_vs_SMC 0.9 10.929 3.08e-08 2.822
HMC_vs_SMC 0.95 7.554 2.65e-06 1.951
HMC_vs_SMC 0.99 4.587 0.000423 1.184
DEMetro_Z_vs_SMC 0.0 17.449 6.78e-11 4.505
DEMetro_Z_vs_SMC 0.3 22.591 2.05e-12 5.833
DEMetro_Z_vs_SMC 0.5 30.871 2.81e-14 7.971
DEMetro_Z_vs_SMC 0.9 32.991 1.12e-14 8.518
DEMetro_Z_vs_SMC 0.95 44.270 1.9e-16 11.431
DEMetro_Z_vs_SMC 0.99 28.476 8.56e-14 7.352
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.382 0.025 0.003 109.645
HMC 0.3 0.415 0.028 0.007 54.207
HMC 0.5 0.417 0.023 0.007 57.288
HMC 0.9 0.214 0.021 0.010 20.145
HMC 0.95 0.156 0.022 0.018 7.605
HMC 0.99 0.142 0.015 0.011 11.306
SMC 0.0 0.027 0.025 0.003 0.410
SMC 0.3 0.026 0.028 0.007 -0.316
SMC 0.5 0.023 0.023 0.007 0.040
SMC 0.9 0.022 0.021 0.010 0.085
SMC 0.95 0.017 0.022 0.018 -0.290
SMC 0.99 0.017 0.015 0.011 0.184
Metro 0.0 0.077 0.025 0.003 15.884
Metro 0.3 0.136 0.028 0.007 15.194
Metro 0.5 0.148 0.023 0.007 18.238
Metro 0.9 0.446 0.021 0.010 44.321
Metro 0.95 0.584 0.022 0.018 31.889
Metro 0.99 1.238 0.015 0.011 109.056
DEMetro_Z 0.0 9.812 0.025 0.003 3009.788
DEMetro_Z 0.3 12.259 0.028 0.007 1711.845
DEMetro_Z 0.5 11.982 0.023 0.007 1736.894
DEMetro_Z 0.9 11.882 0.021 0.010 1237.780
DEMetro_Z 0.95 11.396 0.022 0.018 645.889
DEMetro_Z 0.99 10.342 0.015 0.011 921.289
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.487 0.000511 61.798
HMC 0.3 5.144 0.000149 104.804
HMC 0.5 7.148 4.92e-06 79.194
HMC 0.9 6.282 1.87e-05 17.845
HMC 0.95 4.483 0.00048 9.342
HMC 0.99 5.105 0.00014 9.070
SMC 0.0 0.524 0.605 0.210
SMC 0.3 -0.377 0.709 -0.134
SMC 0.5 -0.225 0.824 -0.067
SMC 0.9 0.553 0.585 0.212
SMC 0.95 -1.023 0.315 -0.339
SMC 0.99 0.248 0.806 0.085
Metro 0.0 4.108 0.00071 3.236
Metro 0.3 3.508 0.00342 11.063
Metro 0.5 5.389 8.11e-05 9.026
Metro 0.9 8.439 6.27e-07 21.140
Metro 0.95 9.902 9.63e-08 35.762
Metro 0.99 19.754 7.05e-12 39.175
DEMetro_Z 0.0 12.355 6.43e-09 1273.919
DEMetro_Z 0.3 11.317 1.98e-08 2150.149
DEMetro_Z 0.5 8.388 7.86e-07 1427.245
DEMetro_Z 0.9 6.159 2.48e-05 1487.958
DEMetro_Z 0.95 10.784 3.64e-08 1580.209
DEMetro_Z 0.99 9.258 2.41e-07 1109.398
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 4.437 0.000563 1.146
HMC_vs_SMC 0.3 5.125 0.000154 1.323
HMC_vs_SMC 0.5 7.186 4.66e-06 1.855
HMC_vs_SMC 0.9 6.289 1.99e-05 1.624
HMC_vs_SMC 0.95 4.635 0.000386 1.197
HMC_vs_SMC 0.99 4.798 0.000284 1.239
Metro_vs_DEMetro_Z 0.0 -12.312 6.72e-09 -3.179
Metro_vs_DEMetro_Z 0.3 -11.142 2.41e-08 -2.877
Metro_vs_DEMetro_Z 0.5 -8.326 8.57e-07 -2.150
Metro_vs_DEMetro_Z 0.9 -6.068 2.9e-05 -1.567
Metro_vs_DEMetro_Z 0.95 -10.557 4.75e-08 -2.726
Metro_vs_DEMetro_Z 0.99 -8.969 3.53e-07 -2.316
HMC_vs_Metro 0.0 4.327 0.000696 1.117
HMC_vs_Metro 0.3 4.436 0.000564 1.145
HMC_vs_Metro 0.5 6.351 1.8e-05 1.640
HMC_vs_Metro 0.9 -0.928 0.369 -0.240
HMC_vs_Metro 0.95 -6.214 2.26e-05 -1.604
HMC_vs_Metro 0.99 -10.671 4.15e-08 -2.755
HMC_vs_DEMetro_Z 0.0 -12.025 9.11e-09 -3.105
HMC_vs_DEMetro_Z 0.3 -11.083 2.58e-08 -2.862
HMC_vs_DEMetro_Z 0.5 -7.991 1.39e-06 -2.063
HMC_vs_DEMetro_Z 0.9 -6.097 2.75e-05 -1.574
HMC_vs_DEMetro_Z 0.95 -10.697 4.03e-08 -2.762
HMC_vs_DEMetro_Z 0.99 -9.177 2.68e-07 -2.369
Metro_vs_SMC 0.0 3.647 0.00264 0.942
Metro_vs_SMC 0.3 3.541 0.00326 0.914
Metro_vs_SMC 0.5 5.263 0.00012 1.359
Metro_vs_SMC 0.9 8.322 8.62e-07 2.149
Metro_vs_SMC 0.95 10.051 8.77e-08 2.595
Metro_vs_SMC 0.99 20.287 8.87e-12 5.238
DEMetro_Z_vs_SMC 0.0 12.352 6.45e-09 3.189
DEMetro_Z_vs_SMC 0.3 11.314 1.98e-08 2.921
DEMetro_Z_vs_SMC 0.5 8.389 7.85e-07 2.166
DEMetro_Z_vs_SMC 0.9 6.158 2.48e-05 1.590
DEMetro_Z_vs_SMC 0.95 10.786 3.63e-08 2.785
DEMetro_Z_vs_SMC 0.99 9.263 2.39e-07 2.392
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.035 0.043 0.016 61.798
HMC 0.3 1.123 0.039 0.010 104.804
HMC 0.5 1.069 0.036 0.013 79.194
HMC 0.9 0.240 0.026 0.012 17.845
HMC 0.95 0.153 0.028 0.013 9.342
HMC 0.99 0.214 0.024 0.021 9.070
SMC 0.0 0.046 0.043 0.016 0.210
SMC 0.3 0.038 0.039 0.010 -0.134
SMC 0.5 0.035 0.036 0.013 -0.067
SMC 0.9 0.029 0.026 0.012 0.212
SMC 0.95 0.024 0.028 0.013 -0.339
SMC 0.99 0.026 0.024 0.021 0.085
Metro 0.0 0.095 0.043 0.016 3.236
Metro 0.3 0.154 0.039 0.010 11.063
Metro 0.5 0.154 0.036 0.013 9.026
Metro 0.9 0.279 0.026 0.012 21.140
Metro 0.95 0.507 0.028 0.013 35.762
Metro 0.99 0.843 0.024 0.021 39.175
DEMetro_Z 0.0 20.490 0.043 0.016 1273.919
DEMetro_Z 0.3 22.283 0.039 0.010 2150.149
DEMetro_Z 0.5 18.657 0.036 0.013 1427.245
DEMetro_Z 0.9 17.807 0.026 0.012 1487.958
DEMetro_Z 0.95 21.182 0.028 0.013 1580.209
DEMetro_Z 0.99 23.204 0.024 0.021 1109.398
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.409 1.63e-05 150.284
HMC 0.3 7.569 2.56e-06 60.012
HMC 0.5 9.628 1.46e-07 76.039
HMC 0.9 9.861 9.81e-08 30.332
HMC 0.95 6.916 5.52e-06 11.546
HMC 0.99 7.400 2.88e-06 16.851
SMC 0.0 1.091 0.289 0.763
SMC 0.3 -0.898 0.379 -0.267
SMC 0.5 -0.435 0.667 -0.146
SMC 0.9 0.104 0.918 0.050
SMC 0.95 -0.862 0.396 -0.292
SMC 0.99 0.146 0.885 0.053
Metro 0.0 4.446 0.000546 21.581
Metro 0.3 5.523 7.15e-05 17.439
Metro 0.5 6.300 1.89e-05 25.903
Metro 0.9 6.818 8.29e-06 67.600
Metro 0.95 6.187 2.34e-05 50.286
Metro 0.99 5.222 0.000129 144.354
DEMetro_Z 0.0 18.066 4.25e-11 4545.565
DEMetro_Z 0.3 24.493 6.78e-13 2044.789
DEMetro_Z 0.5 33.603 8.7e-15 2391.640
DEMetro_Z 0.9 32.482 1.39e-14 1878.697
DEMetro_Z 0.95 39.467 9.3e-16 960.728
DEMetro_Z 0.99 28.139 1.01e-13 1177.297
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -17.971 4.56e-11 -4.640
Metro_vs_DEMetro_Z 0.3 -24.715 6e-13 -6.381
Metro_vs_DEMetro_Z 0.5 -33.652 8.53e-15 -8.689
Metro_vs_DEMetro_Z 0.9 -30.782 2.92e-14 -7.948
Metro_vs_DEMetro_Z 0.95 -37.354 2.01e-15 -9.645
Metro_vs_DEMetro_Z 0.99 -20.749 6.53e-12 -5.357
DEMetro_Z_vs_SMC 0.0 18.055 4.28e-11 4.662
DEMetro_Z_vs_SMC 0.3 24.489 6.8e-13 6.323
DEMetro_Z_vs_SMC 0.5 33.602 8.71e-15 8.676
DEMetro_Z_vs_SMC 0.9 32.373 1.46e-14 8.359
DEMetro_Z_vs_SMC 0.95 39.529 9.16e-16 10.206
DEMetro_Z_vs_SMC 0.99 28.127 1.01e-13 7.262
HMC_vs_DEMetro_Z 0.0 -17.147 8.56e-11 -4.427
HMC_vs_DEMetro_Z 0.3 -23.534 1.17e-12 -6.077
HMC_vs_DEMetro_Z 0.5 -32.576 1.34e-14 -8.411
HMC_vs_DEMetro_Z 0.9 -32.210 1.56e-14 -8.317
HMC_vs_DEMetro_Z 0.95 -39.202 1.03e-15 -10.122
HMC_vs_DEMetro_Z 0.99 -27.329 1.51e-13 -7.056
HMC_vs_Metro 0.0 5.878 4.02e-05 1.518
HMC_vs_Metro 0.3 5.296 0.000113 1.367
HMC_vs_Metro 0.5 7.182 4.7e-06 1.854
HMC_vs_Metro 0.9 -3.783 0.00202 -0.977
HMC_vs_Metro 0.95 -4.338 0.000682 -1.120
HMC_vs_Metro 0.99 -4.567 0.000439 -1.179
HMC_vs_SMC 0.0 6.310 1.92e-05 1.629
HMC_vs_SMC 0.3 7.557 2.64e-06 1.951
HMC_vs_SMC 0.5 9.615 1.52e-07 2.483
HMC_vs_SMC 0.9 10.305 6.43e-08 2.661
HMC_vs_SMC 0.95 7.015 6.1e-06 1.811
HMC_vs_SMC 0.99 7.091 5.42e-06 1.831
Metro_vs_SMC 0.0 4.016 0.00127 1.037
Metro_vs_SMC 0.3 5.524 7.49e-05 1.426
Metro_vs_SMC 0.5 6.218 2.24e-05 1.606
Metro_vs_SMC 0.9 6.741 9.46e-06 1.740
Metro_vs_SMC 0.95 6.181 2.39e-05 1.596
Metro_vs_SMC 0.99 5.237 0.000126 1.352
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.307 0.033 0.002 150.284
HMC 0.3 0.336 0.034 0.005 60.012
HMC 0.5 0.340 0.030 0.004 76.039
HMC 0.9 0.183 0.026 0.005 30.332
HMC 0.95 0.140 0.027 0.010 11.546
HMC 0.99 0.151 0.024 0.008 16.851
SMC 0.0 0.034 0.033 0.002 0.763
SMC 0.3 0.032 0.034 0.005 -0.267
SMC 0.5 0.030 0.030 0.004 -0.146
SMC 0.9 0.027 0.026 0.005 0.050
SMC 0.95 0.024 0.027 0.010 -0.292
SMC 0.99 0.024 0.024 0.008 0.053
Metro 0.0 0.072 0.033 0.002 21.581
Metro 0.3 0.122 0.034 0.005 17.439
Metro 0.5 0.136 0.030 0.004 25.903
Metro 0.9 0.376 0.026 0.005 67.600
Metro 0.95 0.520 0.027 0.010 50.286
Metro 0.99 1.113 0.024 0.008 144.354
DEMetro_Z 0.0 8.337 0.033 0.002 4545.565
DEMetro_Z 0.3 10.338 0.034 0.005 2044.789
DEMetro_Z 0.5 9.761 0.030 0.004 2391.640
DEMetro_Z 0.9 9.738 0.026 0.005 1878.697
DEMetro_Z 0.95 9.440 0.027 0.010 960.728
DEMetro_Z 0.99 8.906 0.024 0.008 1177.297
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.373 1.73e-05 117.245
HMC 0.3 7.558 2.61e-06 62.547
HMC 0.5 9.635 1.46e-07 94.656
HMC 0.9 11.384 1.55e-08 32.918
HMC 0.95 6.891 6.09e-06 12.998
HMC 0.99 7.780 1.46e-06 14.101
SMC 0.0 1.013 0.323 0.632
SMC 0.3 -1.223 0.234 -0.373
SMC 0.5 0.070 0.945 0.029
SMC 0.9 0.036 0.972 0.014
SMC 0.95 -0.886 0.384 -0.285
SMC 0.99 0.354 0.726 0.117
Metro 0.0 4.646 0.000369 16.814
Metro 0.3 5.728 4.94e-05 17.368
Metro 0.5 6.980 6.18e-06 29.311
Metro 0.9 8.839 4.09e-07 53.190
Metro 0.95 7.470 2.96e-06 51.268
Metro 0.99 10.079 8.39e-08 112.907
DEMetro_Z 0.0 85.684 1.74e-20 656.800
DEMetro_Z 0.3 86.632 1.1e-20 308.964
DEMetro_Z 0.5 33.225 1e-14 456.336
DEMetro_Z 0.9 66.756 4.37e-19 240.818
DEMetro_Z 0.95 64.220 4.34e-19 143.662
DEMetro_Z 0.99 82.433 7.67e-21 152.999
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 85.567 1.93e-20 22.093
DEMetro_Z_vs_SMC 0.3 86.727 1.6e-20 22.393
DEMetro_Z_vs_SMC 0.5 33.314 9.81e-15 8.602
DEMetro_Z_vs_SMC 0.9 65.417 8.22e-19 16.891
DEMetro_Z_vs_SMC 0.95 65.273 8.48e-19 16.853
DEMetro_Z_vs_SMC 0.99 79.741 5.18e-20 20.589
HMC_vs_Metro 0.0 5.927 3.69e-05 1.530
HMC_vs_Metro 0.3 5.200 0.000134 1.343
HMC_vs_Metro 0.5 7.156 4.89e-06 1.848
HMC_vs_Metro 0.9 -3.338 0.00488 -0.862
HMC_vs_Metro 0.95 -4.916 0.000227 -1.269
HMC_vs_Metro 0.99 -8.696 5.12e-07 -2.245
Metro_vs_DEMetro_Z 0.0 -81.021 4.15e-20 -20.919
Metro_vs_DEMetro_Z 0.3 -59.842 2.85e-18 -15.451
Metro_vs_DEMetro_Z 0.5 -31.139 2.49e-14 -8.040
Metro_vs_DEMetro_Z 0.9 -24.825 5.64e-13 -6.410
Metro_vs_DEMetro_Z 0.95 -14.317 9.42e-10 -3.697
Metro_vs_DEMetro_Z 0.99 -3.733 0.00223 -0.964
HMC_vs_SMC 0.0 6.252 2.12e-05 1.614
HMC_vs_SMC 0.3 7.586 2.53e-06 1.959
HMC_vs_SMC 0.5 9.584 1.58e-07 2.475
HMC_vs_SMC 0.9 11.472 1.66e-08 2.962
HMC_vs_SMC 0.95 7.066 5.63e-06 1.824
HMC_vs_SMC 0.99 7.240 4.29e-06 1.869
Metro_vs_SMC 0.0 4.129 0.00102 1.066
Metro_vs_SMC 0.3 5.756 4.97e-05 1.486
Metro_vs_SMC 0.5 6.785 8.8e-06 1.752
Metro_vs_SMC 0.9 8.766 4.65e-07 2.263
Metro_vs_SMC 0.95 7.455 3.08e-06 1.925
Metro_vs_SMC 0.99 10.069 8.58e-08 2.600
HMC_vs_DEMetro_Z 0.0 -27.059 1.73e-13 -6.987
HMC_vs_DEMetro_Z 0.3 -25.465 3.98e-13 -6.575
HMC_vs_DEMetro_Z 0.5 -19.693 1.33e-11 -5.085
HMC_vs_DEMetro_Z 0.9 -39.928 7.97e-16 -10.309
HMC_vs_DEMetro_Z 0.95 -39.459 9.39e-16 -10.188
HMC_vs_DEMetro_Z 0.99 -60.548 2.42e-18 -15.634
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.174 0.013 0.001 117.245
HMC 0.3 0.201 0.015 0.003 62.547
HMC 0.5 0.215 0.013 0.002 94.656
HMC 0.9 0.142 0.014 0.004 32.918
HMC 0.95 0.100 0.016 0.006 12.998
HMC 0.99 0.101 0.014 0.006 14.101
SMC 0.0 0.014 0.013 0.001 0.632
SMC 0.3 0.014 0.015 0.003 -0.373
SMC 0.5 0.014 0.013 0.002 0.029
SMC 0.9 0.014 0.014 0.004 0.014
SMC 0.95 0.014 0.016 0.006 -0.285
SMC 0.99 0.015 0.014 0.006 0.117
Metro 0.0 0.036 0.013 0.001 16.814
Metro 0.3 0.066 0.015 0.003 17.368
Metro 0.5 0.076 0.013 0.002 29.311
Metro 0.9 0.221 0.014 0.004 53.190
Metro 0.95 0.348 0.016 0.006 51.268
Metro 0.99 0.708 0.014 0.006 112.907
DEMetro_Z 0.0 0.914 0.013 0.001 656.800
DEMetro_Z 0.3 0.933 0.015 0.003 308.964
DEMetro_Z 0.5 0.986 0.013 0.002 456.336
DEMetro_Z 0.9 0.949 0.014 0.004 240.818
DEMetro_Z 0.95 0.948 0.016 0.006 143.662
DEMetro_Z 0.99 0.954 0.014 0.006 152.999
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99

Vary_Correlation_with_Tails_and_MM (Mixture, correlation, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 3.551 0.00223 2.477
HMC 0.3 3.804 0.00175 5.531
HMC 0.5 0.304 0.764 0.095
HMC 0.9 1.097 0.291 2.277
HMC 0.95 1.907 0.0722 1.306
HMC 0.99 3.635 0.00146 1.916
SMC 0.0 4.352 0.000562 5.818
SMC 0.3 4.925 0.000191 7.677
SMC 0.5 2.730 0.0127 1.596
SMC 0.9 2.487 0.0191 0.925
SMC 0.95 2.618 0.0173 1.840
SMC 0.99 2.398 0.025 1.198
Metro 0.0 3.307 0.00389 2.358
Metro 0.3 5.961 2.17e-05 6.471
Metro 0.5 1.726 0.0957 0.580
Metro 0.9 2.176 0.0406 1.161
Metro 0.95 2.595 0.0202 3.340
Metro 0.99 2.469 0.027 34.716
DEMetro_Z 0.0 5.143 0.000111 6.146
DEMetro_Z 0.3 4.122 0.000838 4.563
DEMetro_Z 0.5 3.397 0.00278 1.968
DEMetro_Z 0.9 3.514 0.0019 1.794
DEMetro_Z 0.95 3.826 0.00171 6.488
DEMetro_Z 0.99 2.683 0.0157 2.221
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -2.817 0.0137 -0.727
HMC_vs_DEMetro_Z 0.3 0.580 0.571 0.150
HMC_vs_DEMetro_Z 0.5 -3.235 0.00599 -0.835
HMC_vs_DEMetro_Z 0.9 0.260 0.799 0.067
HMC_vs_DEMetro_Z 0.95 -2.737 0.0161 -0.707
HMC_vs_DEMetro_Z 0.99 -0.316 0.757 -0.082
Metro_vs_SMC 0.0 -2.387 0.0316 -0.616
Metro_vs_SMC 0.3 -0.680 0.508 -0.176
Metro_vs_SMC 0.5 -2.067 0.0577 -0.534
Metro_vs_SMC 0.9 0.425 0.677 0.110
Metro_vs_SMC 0.95 0.932 0.367 0.241
Metro_vs_SMC 0.99 2.378 0.0322 0.614
Metro_vs_DEMetro_Z 0.0 -3.320 0.00505 -0.857
Metro_vs_DEMetro_Z 0.3 1.146 0.271 0.296
Metro_vs_DEMetro_Z 0.5 -2.801 0.0142 -0.723
Metro_vs_DEMetro_Z 0.9 -0.928 0.369 -0.240
Metro_vs_DEMetro_Z 0.95 -1.726 0.106 -0.446
Metro_vs_DEMetro_Z 0.99 2.273 0.0393 0.587
HMC_vs_Metro 0.0 0.103 0.919 0.027
HMC_vs_Metro 0.3 -0.620 0.545 -0.160
HMC_vs_Metro 0.5 -1.628 0.126 -0.420
HMC_vs_Metro 0.9 0.505 0.621 0.131
HMC_vs_Metro 0.95 -1.403 0.182 -0.362
HMC_vs_Metro 0.99 -2.351 0.0339 -0.607
HMC_vs_SMC 0.0 -2.251 0.041 -0.581
HMC_vs_SMC 0.3 -0.902 0.382 -0.233
HMC_vs_SMC 0.5 -2.772 0.015 -0.716
HMC_vs_SMC 0.9 0.636 0.535 0.164
HMC_vs_SMC 0.95 -0.680 0.508 -0.175
HMC_vs_SMC 0.99 1.632 0.125 0.421
DEMetro_Z_vs_SMC 0.0 0.248 0.807 0.064
DEMetro_Z_vs_SMC 0.3 -2.403 0.0307 -0.620
DEMetro_Z_vs_SMC 0.5 0.469 0.646 0.121
DEMetro_Z_vs_SMC 0.9 1.426 0.176 0.368
DEMetro_Z_vs_SMC 0.95 2.535 0.0238 0.655
DEMetro_Z_vs_SMC 0.99 1.106 0.287 0.286
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.148 0.050 0.039 2.477
HMC 0.3 0.228 0.068 0.029 5.531
HMC 0.5 0.118 0.109 0.095 0.095
HMC 0.9 0.391 0.099 0.128 2.277
HMC 0.95 0.116 0.068 0.037 1.306
HMC 0.99 0.124 0.047 0.040 1.916
SMC 0.0 0.280 0.050 0.039 5.818
SMC 0.3 0.290 0.068 0.029 7.677
SMC 0.5 0.260 0.109 0.095 1.596
SMC 0.9 0.217 0.099 0.128 0.925
SMC 0.95 0.136 0.068 0.037 1.840
SMC 0.99 0.095 0.047 0.040 1.198
Metro 0.0 0.143 0.050 0.039 2.358
Metro 0.3 0.255 0.068 0.029 6.471
Metro 0.5 0.163 0.109 0.095 0.580
Metro 0.9 0.248 0.099 0.128 1.161
Metro 0.95 0.191 0.068 0.037 3.340
Metro 0.99 1.434 0.047 0.040 34.716
DEMetro_Z 0.0 0.293 0.050 0.039 6.146
DEMetro_Z 0.3 0.200 0.068 0.029 4.563
DEMetro_Z 0.5 0.295 0.109 0.095 1.968
DEMetro_Z 0.9 0.329 0.099 0.128 1.794
DEMetro_Z 0.95 0.306 0.068 0.037 6.488
DEMetro_Z 0.99 0.136 0.047 0.040 2.221
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.468 0.164 -0.381
HMC 0.3 1.358 0.194 1.577
HMC 0.5 -1.024 0.323 -0.265
HMC 0.9 0.611 0.549 0.405
HMC 0.95 0.243 0.811 0.189
HMC 0.99 0.725 0.475 0.320
SMC 0.0 -1.379 0.189 -0.357
SMC 0.3 3.075 0.00718 2.946
SMC 0.5 -0.979 0.344 -0.253
SMC 0.9 -0.019 0.985 -0.005
SMC 0.95 1.070 0.298 0.721
SMC 0.99 3.423 0.00229 1.681
Metro 0.0 -1.514 0.152 -0.393
Metro 0.3 1.833 0.0855 1.855
Metro 0.5 -1.032 0.319 -0.267
Metro 0.9 -0.843 0.413 -0.219
Metro 0.95 0.478 0.639 0.388
Metro 0.99 1.341 0.201 11.139
DEMetro_Z 0.0 -1.399 0.183 -0.363
DEMetro_Z 0.3 3.074 0.00509 1.405
DEMetro_Z 0.5 -1.025 0.323 -0.265
DEMetro_Z 0.9 -0.750 0.465 -0.195
DEMetro_Z 0.95 0.532 0.602 0.431
DEMetro_Z 0.99 0.709 0.484 0.275
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -1.180 0.258 -0.305
HMC_vs_SMC 0.3 -0.840 0.415 -0.217
HMC_vs_SMC 0.5 -1.364 0.194 -0.352
HMC_vs_SMC 0.9 0.674 0.511 0.174
HMC_vs_SMC 0.95 -2.099 0.0544 -0.542
HMC_vs_SMC 0.99 -3.281 0.00547 -0.847
Metro_vs_DEMetro_Z 0.0 -2.953 0.0105 -0.762
Metro_vs_DEMetro_Z 0.3 0.452 0.658 0.117
Metro_vs_DEMetro_Z 0.5 -0.262 0.797 -0.068
Metro_vs_DEMetro_Z 0.9 -1.039 0.317 -0.268
Metro_vs_DEMetro_Z 0.95 -0.640 0.533 -0.165
Metro_vs_DEMetro_Z 0.99 1.308 0.212 0.338
HMC_vs_Metro 0.0 1.114 0.284 0.288
HMC_vs_Metro 0.3 -0.193 0.85 -0.050
HMC_vs_Metro 0.5 0.266 0.794 0.069
HMC_vs_Metro 0.9 1.018 0.326 0.263
HMC_vs_Metro 0.95 -3.317 0.00509 -0.856
HMC_vs_Metro 0.99 -1.296 0.216 -0.335
HMC_vs_DEMetro_Z 0.0 -2.785 0.0146 -0.719
HMC_vs_DEMetro_Z 0.3 0.139 0.891 0.036
HMC_vs_DEMetro_Z 0.5 0.021 0.984 0.005
HMC_vs_DEMetro_Z 0.9 0.983 0.342 0.254
HMC_vs_DEMetro_Z 0.95 -3.223 0.00613 -0.832
HMC_vs_DEMetro_Z 0.99 0.263 0.797 0.068
Metro_vs_SMC 0.0 -1.759 0.1 -0.454
Metro_vs_SMC 0.3 -0.790 0.442 -0.204
Metro_vs_SMC 0.5 -1.801 0.0932 -0.465
Metro_vs_SMC 0.9 -4.460 0.000539 -1.151
Metro_vs_SMC 0.95 -1.216 0.244 -0.314
Metro_vs_SMC 0.99 1.123 0.28 0.290
DEMetro_Z_vs_SMC 0.0 -0.287 0.779 -0.074
DEMetro_Z_vs_SMC 0.3 -1.596 0.133 -0.412
DEMetro_Z_vs_SMC 0.5 -1.185 0.256 -0.306
DEMetro_Z_vs_SMC 0.9 -3.985 0.00135 -1.029
DEMetro_Z_vs_SMC 0.95 -1.087 0.295 -0.281
DEMetro_Z_vs_SMC 0.99 -2.899 0.0117 -0.749
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.510 22.041 46.008 -0.381
HMC 0.3 4.045 2.136 1.210 1.577
HMC 0.5 4.454 46.852 160.247 -0.265
HMC 0.9 178.516 71.206 264.663 0.405
HMC 0.95 11.906 9.573 12.329 0.189
HMC 0.99 6.057 4.221 5.737 0.320
SMC 0.0 5.601 22.041 46.008 -0.357
SMC 0.3 5.702 2.136 1.210 2.946
SMC 0.5 6.323 46.852 160.247 -0.253
SMC 0.9 69.901 71.206 264.663 -0.005
SMC 0.95 18.466 9.573 12.329 0.721
SMC 0.99 13.866 4.221 5.737 1.681
Metro 0.0 3.964 22.041 46.008 -0.393
Metro 0.3 4.382 2.136 1.210 1.855
Metro 0.5 4.136 46.852 160.247 -0.267
Metro 0.9 13.273 71.206 264.663 -0.219
Metro 0.95 14.357 9.573 12.329 0.388
Metro 0.99 68.131 4.221 5.737 11.139
DEMetro_Z 0.0 5.329 22.041 46.008 -0.363
DEMetro_Z 0.3 3.836 2.136 1.210 1.405
DEMetro_Z 0.5 4.434 46.852 160.247 -0.265
DEMetro_Z 0.9 19.528 71.206 264.663 -0.195
DEMetro_Z 0.95 14.889 9.573 12.329 0.431
DEMetro_Z 0.99 5.800 4.221 5.737 0.275
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.666 0.0131 1.154
HMC 0.3 4.268 0.000665 5.700
HMC 0.5 2.024 0.0538 0.636
HMC 0.9 1.274 0.223 2.908
HMC 0.95 2.139 0.0476 1.872
HMC 0.99 4.954 0.000124 4.194
SMC 0.0 5.426 3.7e-05 3.909
SMC 0.3 8.095 8.5e-07 13.243
SMC 0.5 6.601 1.38e-06 3.594
SMC 0.9 10.060 5.78e-08 17.372
SMC 0.95 7.810 1.43e-06 14.851
SMC 0.99 7.413 3.04e-06 23.527
Metro 0.0 4.345 0.000167 1.642
Metro 0.3 5.889 2.62e-05 6.785
Metro 0.5 3.214 0.00353 1.024
Metro 0.9 4.794 5.99e-05 2.097
Metro 0.95 4.850 0.000158 4.233
Metro 0.99 2.377 0.0323 48.337
DEMetro_Z 0.0 6.296 3.51e-06 3.695
DEMetro_Z 0.3 7.329 1.78e-06 7.556
DEMetro_Z 0.5 5.461 1.9e-05 2.984
DEMetro_Z 0.9 5.376 2.9e-05 3.233
DEMetro_Z 0.95 5.467 5.88e-05 6.409
DEMetro_Z 0.99 8.167 2.94e-07 6.915
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -3.657 0.00259 -0.944
Metro_vs_DEMetro_Z 0.3 -0.872 0.398 -0.225
Metro_vs_DEMetro_Z 0.5 -4.225 0.000849 -1.091
Metro_vs_DEMetro_Z 0.9 -1.800 0.0934 -0.465
Metro_vs_DEMetro_Z 0.95 -1.748 0.102 -0.451
Metro_vs_DEMetro_Z 0.99 2.013 0.0637 0.520
DEMetro_Z_vs_SMC 0.0 -0.357 0.727 -0.092
DEMetro_Z_vs_SMC 0.3 -4.225 0.000848 -1.091
DEMetro_Z_vs_SMC 0.5 -0.823 0.424 -0.213
DEMetro_Z_vs_SMC 0.9 -8.916 3.8e-07 -2.302
DEMetro_Z_vs_SMC 0.95 -4.865 0.00025 -1.256
DEMetro_Z_vs_SMC 0.99 -4.947 0.000215 -1.277
HMC_vs_DEMetro_Z 0.0 -4.171 0.000942 -1.077
HMC_vs_DEMetro_Z 0.3 -1.144 0.272 -0.295
HMC_vs_DEMetro_Z 0.5 -4.360 0.000653 -1.126
HMC_vs_DEMetro_Z 0.9 -0.157 0.878 -0.040
HMC_vs_DEMetro_Z 0.95 -3.166 0.00686 -0.818
HMC_vs_DEMetro_Z 0.99 -3.403 0.00429 -0.879
HMC_vs_Metro 0.0 -1.101 0.29 -0.284
HMC_vs_Metro 0.3 -0.699 0.496 -0.180
HMC_vs_Metro 0.5 -1.447 0.17 -0.374
HMC_vs_Metro 0.9 0.347 0.734 0.090
HMC_vs_Metro 0.95 -1.938 0.073 -0.500
HMC_vs_Metro 0.99 -2.166 0.0481 -0.559
HMC_vs_SMC 0.0 -3.402 0.0043 -0.878
HMC_vs_SMC 0.3 -3.016 0.00926 -0.779
HMC_vs_SMC 0.5 -5.030 0.000184 -1.299
HMC_vs_SMC 0.9 -5.910 3.8e-05 -1.526
HMC_vs_SMC 0.95 -6.350 1.8e-05 -1.640
HMC_vs_SMC 0.99 -6.422 1.59e-05 -1.658
Metro_vs_SMC 0.0 -3.532 0.00332 -0.912
Metro_vs_SMC 0.3 -4.287 0.000752 -1.107
Metro_vs_SMC 0.5 -4.917 0.000227 -1.269
Metro_vs_SMC 0.9 -8.493 6.78e-07 -2.193
Metro_vs_SMC 0.95 -5.290 0.000114 -1.366
Metro_vs_SMC 0.99 1.179 0.258 0.304
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.231 0.148 0.071 1.154
HMC 0.3 0.293 0.136 0.028 5.700
HMC 0.5 0.215 0.160 0.087 0.636
HMC 0.9 0.473 0.144 0.113 2.908
HMC 0.95 0.206 0.135 0.038 1.872
HMC 0.99 0.220 0.098 0.029 4.194
SMC 0.0 0.427 0.148 0.071 3.909
SMC 0.3 0.501 0.136 0.028 13.243
SMC 0.5 0.471 0.160 0.087 3.594
SMC 0.9 2.109 0.144 0.113 17.372
SMC 0.95 0.697 0.135 0.038 14.851
SMC 0.99 0.778 0.098 0.029 23.527
Metro 0.0 0.265 0.148 0.071 1.642
Metro 0.3 0.323 0.136 0.028 6.785
Metro 0.5 0.249 0.160 0.087 1.024
Metro 0.9 0.381 0.144 0.113 2.097
Metro 0.95 0.296 0.135 0.038 4.233
Metro 0.99 1.495 0.098 0.029 48.337
DEMetro_Z 0.0 0.412 0.148 0.071 3.695
DEMetro_Z 0.3 0.344 0.136 0.028 7.556
DEMetro_Z 0.5 0.418 0.160 0.087 2.984
DEMetro_Z 0.9 0.510 0.144 0.113 3.233
DEMetro_Z 0.95 0.378 0.135 0.038 6.409
DEMetro_Z 0.99 0.298 0.098 0.029 6.915
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 3.314 0.00443 3.430
HMC 0.3 3.926 0.00136 5.689
HMC 0.5 2.650 0.0158 1.742
HMC 0.9 3.969 0.00106 3.694
HMC 0.95 5.097 7.12e-05 3.557
HMC 0.99 4.367 0.000542 5.719
SMC 0.0 4.603 0.000365 7.786
SMC 0.3 6.346 1.4e-05 9.802
SMC 0.5 5.851 3.11e-05 7.803
SMC 0.9 14.616 6.43e-10 59.420
SMC 0.95 11.232 1.65e-08 25.049
SMC 0.99 10.743 3.48e-08 40.505
Metro 0.0 4.991 7.73e-05 3.174
Metro 0.3 4.478 0.000374 4.332
Metro 0.5 4.913 6.91e-05 2.672
Metro 0.9 12.559 5.97e-10 10.775
Metro 0.95 4.939 0.000174 6.485
Metro 0.99 5.811 4.44e-05 31.107
DEMetro_Z 0.0 5.826 3.51e-05 8.998
DEMetro_Z 0.3 4.330 0.000576 5.481
DEMetro_Z 0.5 4.389 0.000553 7.247
DEMetro_Z 0.9 5.591 6.27e-05 16.189
DEMetro_Z 0.95 5.888 3.43e-05 11.656
DEMetro_Z 0.99 7.606 1.85e-06 13.070
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 0.814 0.429 0.210
DEMetro_Z_vs_SMC 0.3 -3.173 0.00677 -0.819
DEMetro_Z_vs_SMC 0.5 -0.251 0.806 -0.065
DEMetro_Z_vs_SMC 0.9 -11.486 1.64e-08 -2.966
DEMetro_Z_vs_SMC 0.95 -5.812 4.51e-05 -1.501
DEMetro_Z_vs_SMC 0.99 -6.424 1.59e-05 -1.659
HMC_vs_Metro 0.0 0.231 0.821 0.060
HMC_vs_Metro 0.3 0.914 0.376 0.236
HMC_vs_Metro 0.5 -1.278 0.222 -0.330
HMC_vs_Metro 0.9 -5.270 0.000118 -1.361
HMC_vs_Metro 0.95 -1.981 0.0676 -0.511
HMC_vs_Metro 0.99 -4.476 0.000523 -1.156
Metro_vs_DEMetro_Z 0.0 -3.699 0.00238 -0.955
Metro_vs_DEMetro_Z 0.3 -0.813 0.43 -0.210
Metro_vs_DEMetro_Z 0.5 -3.049 0.00867 -0.787
Metro_vs_DEMetro_Z 0.9 -1.684 0.114 -0.435
Metro_vs_DEMetro_Z 0.95 -2.086 0.0557 -0.539
Metro_vs_DEMetro_Z 0.99 3.024 0.00911 0.781
HMC_vs_SMC 0.0 -2.146 0.0499 -0.554
HMC_vs_SMC 0.3 -1.834 0.0879 -0.474
HMC_vs_SMC 0.5 -3.804 0.00194 -0.982
HMC_vs_SMC 0.9 -12.943 3.52e-09 -3.342
HMC_vs_SMC 0.95 -9.449 1.88e-07 -2.440
HMC_vs_SMC 0.99 -8.600 5.84e-07 -2.221
Metro_vs_SMC 0.0 -2.756 0.0155 -0.712
Metro_vs_SMC 0.3 -4.093 0.0011 -1.057
Metro_vs_SMC 0.5 -3.477 0.0037 -0.898
Metro_vs_SMC 0.9 -12.007 9.29e-09 -3.100
Metro_vs_SMC 0.95 -6.594 1.2e-05 -1.703
Metro_vs_SMC 0.99 -1.320 0.208 -0.341
HMC_vs_DEMetro_Z 0.0 -3.092 0.00795 -0.798
HMC_vs_DEMetro_Z 0.3 0.107 0.916 0.028
HMC_vs_DEMetro_Z 0.5 -3.315 0.00511 -0.856
HMC_vs_DEMetro_Z 0.9 -4.345 0.000672 -1.122
HMC_vs_DEMetro_Z 0.95 -4.318 0.000708 -1.115
HMC_vs_DEMetro_Z 0.99 -5.288 0.000115 -1.365
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.010 0.005 3.430
HMC 0.3 0.042 0.014 0.005 5.689
HMC 0.5 0.024 0.013 0.006 1.742
HMC 0.9 0.028 0.014 0.004 3.694
HMC 0.95 0.030 0.014 0.004 3.557
HMC 0.99 0.032 0.012 0.003 5.719
SMC 0.0 0.050 0.010 0.005 7.786
SMC 0.3 0.062 0.014 0.005 9.802
SMC 0.5 0.060 0.013 0.006 7.803
SMC 0.9 0.235 0.014 0.004 59.420
SMC 0.95 0.125 0.014 0.004 25.049
SMC 0.99 0.153 0.012 0.003 40.505
Metro 0.0 0.026 0.010 0.005 3.174
Metro 0.3 0.035 0.014 0.005 4.332
Metro 0.5 0.029 0.013 0.006 2.672
Metro 0.9 0.054 0.014 0.004 10.775
Metro 0.95 0.043 0.014 0.004 6.485
Metro 0.99 0.121 0.012 0.003 31.107
DEMetro_Z 0.0 0.057 0.010 0.005 8.998
DEMetro_Z 0.3 0.040 0.014 0.005 5.481
DEMetro_Z 0.5 0.056 0.013 0.006 7.247
DEMetro_Z 0.9 0.074 0.014 0.004 16.189
DEMetro_Z 0.95 0.066 0.014 0.004 11.656
DEMetro_Z 0.99 0.058 0.012 0.003 13.070
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.396 0.000383 3.510
HMC 0.3 3.617 0.00246 4.401
HMC 0.5 2.040 0.0517 0.886
HMC 0.9 1.605 0.12 0.536
HMC 0.95 1.317 0.207 1.385
HMC 0.99 3.192 0.00444 1.829
SMC 0.0 4.437 0.000425 4.631
SMC 0.3 2.426 0.029 5.659
SMC 0.5 1.619 0.122 1.111
SMC 0.9 4.272 0.000504 3.431
SMC 0.95 3.175 0.00611 3.756
SMC 0.99 3.538 0.00165 1.650
Metro 0.0 3.457 0.00351 4.762
Metro 0.3 3.170 0.00637 4.536
Metro 0.5 2.069 0.048 0.776
Metro 0.9 1.948 0.0617 0.762
Metro 0.95 2.577 0.0216 6.189
Metro 0.99 1.644 0.122 56.649
DEMetro_Z 0.0 4.509 0.000199 2.591
DEMetro_Z 0.3 3.190 0.00615 4.752
DEMetro_Z 0.5 1.720 0.0967 0.589
DEMetro_Z 0.9 2.082 0.0466 0.755
DEMetro_Z 0.95 3.283 0.00466 3.218
DEMetro_Z 0.99 3.273 0.00496 3.784
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 0.974 0.346 0.252
HMC_vs_DEMetro_Z 0.3 -0.177 0.862 -0.046
HMC_vs_DEMetro_Z 0.5 0.767 0.456 0.198
HMC_vs_DEMetro_Z 0.9 -0.549 0.592 -0.142
HMC_vs_DEMetro_Z 0.95 -1.203 0.249 -0.310
HMC_vs_DEMetro_Z 0.99 -1.882 0.0807 -0.486
Metro_vs_SMC 0.0 0.107 0.916 0.028
Metro_vs_SMC 0.3 -0.391 0.702 -0.101
Metro_vs_SMC 0.5 -0.528 0.606 -0.136
Metro_vs_SMC 0.9 -2.830 0.0134 -0.731
Metro_vs_SMC 0.95 0.872 0.398 0.225
Metro_vs_SMC 0.99 1.598 0.132 0.413
Metro_vs_DEMetro_Z 0.0 1.507 0.154 0.389
Metro_vs_DEMetro_Z 0.3 -0.089 0.93 -0.023
Metro_vs_DEMetro_Z 0.5 0.465 0.649 0.120
Metro_vs_DEMetro_Z 0.9 0.014 0.989 0.004
Metro_vs_DEMetro_Z 0.95 1.140 0.274 0.294
Metro_vs_DEMetro_Z 0.99 1.528 0.149 0.394
HMC_vs_Metro 0.0 -0.750 0.466 -0.194
HMC_vs_Metro 0.3 -0.088 0.931 -0.023
HMC_vs_Metro 0.5 0.300 0.769 0.077
HMC_vs_Metro 0.9 -0.825 0.423 -0.213
HMC_vs_Metro 0.95 -1.887 0.0801 -0.487
HMC_vs_Metro 0.99 -1.599 0.132 -0.413
HMC_vs_SMC 0.0 -0.796 0.439 -0.206
HMC_vs_SMC 0.3 -0.442 0.665 -0.114
HMC_vs_SMC 0.5 -0.403 0.693 -0.104
HMC_vs_SMC 0.9 -3.639 0.00268 -0.940
HMC_vs_SMC 0.95 -1.490 0.158 -0.385
HMC_vs_SMC 0.99 0.329 0.747 0.085
DEMetro_Z_vs_SMC 0.0 -1.584 0.136 -0.409
DEMetro_Z_vs_SMC 0.3 -0.435 0.67 -0.112
DEMetro_Z_vs_SMC 0.5 -0.906 0.38 -0.234
DEMetro_Z_vs_SMC 0.9 -3.104 0.00776 -0.802
DEMetro_Z_vs_SMC 0.95 -0.325 0.75 -0.084
DEMetro_Z_vs_SMC 0.99 1.840 0.0871 0.475
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.189 0.050 0.039 3.510
HMC 0.3 0.195 0.068 0.029 4.401
HMC 0.5 0.192 0.109 0.095 0.886
HMC 0.9 0.167 0.099 0.128 0.536
HMC 0.95 0.119 0.068 0.037 1.385
HMC 0.99 0.120 0.047 0.040 1.829
SMC 0.0 0.233 0.050 0.039 4.631
SMC 0.3 0.231 0.068 0.029 5.659
SMC 0.5 0.214 0.109 0.095 1.111
SMC 0.9 0.539 0.099 0.128 3.431
SMC 0.95 0.206 0.068 0.037 3.756
SMC 0.99 0.113 0.047 0.040 1.650
Metro 0.0 0.238 0.050 0.039 4.762
Metro 0.3 0.199 0.068 0.029 4.536
Metro 0.5 0.182 0.109 0.095 0.776
Metro 0.9 0.196 0.099 0.128 0.762
Metro 0.95 0.295 0.068 0.037 6.189
Metro 0.99 2.310 0.047 0.040 56.649
DEMetro_Z 0.0 0.152 0.050 0.039 2.591
DEMetro_Z 0.3 0.205 0.068 0.029 4.752
DEMetro_Z 0.5 0.164 0.109 0.095 0.589
DEMetro_Z 0.9 0.196 0.099 0.128 0.755
DEMetro_Z 0.95 0.186 0.068 0.037 3.218
DEMetro_Z 0.99 0.199 0.047 0.040 3.784
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.455 0.167 -0.377
HMC 0.3 1.265 0.226 3.263
HMC 0.5 -1.062 0.306 -0.274
HMC 0.9 -0.846 0.411 -0.220
HMC 0.95 0.608 0.551 0.484
HMC 0.99 0.699 0.491 0.319
SMC 0.0 -1.392 0.185 -0.361
SMC 0.3 1.521 0.144 0.932
SMC 0.5 -1.037 0.317 -0.268
SMC 0.9 -0.732 0.476 -0.189
SMC 0.95 0.453 0.656 0.342
SMC 0.99 0.752 0.458 0.268
Metro 0.0 -1.282 0.219 -0.338
Metro 0.3 0.938 0.358 0.488
Metro 0.5 -1.019 0.326 -0.263
Metro 0.9 -0.840 0.415 -0.218
Metro 0.95 0.333 0.743 0.232
Metro 0.99 1.498 0.156 10.229
DEMetro_Z 0.0 -1.428 0.175 -0.371
DEMetro_Z 0.3 3.540 0.0016 1.608
DEMetro_Z 0.5 -1.038 0.317 -0.268
DEMetro_Z 0.9 -0.839 0.415 -0.218
DEMetro_Z 0.95 0.464 0.648 0.374
DEMetro_Z 0.99 1.140 0.27 1.014
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -1.099 0.29 -0.284
HMC_vs_SMC 0.3 0.911 0.378 0.235
HMC_vs_SMC 0.5 -1.439 0.172 -0.371
HMC_vs_SMC 0.9 -1.290 0.218 -0.333
HMC_vs_SMC 0.95 0.895 0.386 0.231
HMC_vs_SMC 0.99 0.155 0.879 0.040
Metro_vs_DEMetro_Z 0.0 1.039 0.316 0.268
Metro_vs_DEMetro_Z 0.3 -4.022 0.00126 -1.039
Metro_vs_DEMetro_Z 0.5 0.810 0.431 0.209
Metro_vs_DEMetro_Z 0.9 -0.082 0.936 -0.021
Metro_vs_DEMetro_Z 0.95 -1.150 0.269 -0.297
Metro_vs_DEMetro_Z 0.99 1.326 0.206 0.342
HMC_vs_Metro 0.0 -1.154 0.268 -0.298
HMC_vs_Metro 0.3 1.064 0.305 0.275
HMC_vs_Metro 0.5 -2.180 0.0469 -0.563
HMC_vs_Metro 0.9 -0.397 0.697 -0.103
HMC_vs_Metro 0.95 1.849 0.0857 0.477
HMC_vs_Metro 0.99 -1.435 0.173 -0.371
HMC_vs_DEMetro_Z 0.0 -0.679 0.508 -0.175
HMC_vs_DEMetro_Z 0.3 0.648 0.527 0.167
HMC_vs_DEMetro_Z 0.5 -3.486 0.00363 -0.900
HMC_vs_DEMetro_Z 0.9 -0.478 0.64 -0.123
HMC_vs_DEMetro_Z 0.95 1.140 0.273 0.294
HMC_vs_DEMetro_Z 0.99 -0.828 0.422 -0.214
Metro_vs_SMC 0.0 0.579 0.572 0.149
Metro_vs_SMC 0.3 -0.936 0.365 -0.242
Metro_vs_SMC 0.5 0.696 0.498 0.180
Metro_vs_SMC 0.9 -1.266 0.226 -0.327
Metro_vs_SMC 0.95 -0.710 0.489 -0.183
Metro_vs_SMC 0.99 1.452 0.168 0.375
DEMetro_Z_vs_SMC 0.0 -0.697 0.497 -0.180
DEMetro_Z_vs_SMC 0.3 1.354 0.197 0.350
DEMetro_Z_vs_SMC 0.5 -0.016 0.987 -0.004
DEMetro_Z_vs_SMC 0.9 -1.236 0.237 -0.319
DEMetro_Z_vs_SMC 0.95 0.227 0.823 0.059
DEMetro_Z_vs_SMC 0.99 0.848 0.411 0.219
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.677 22.041 46.008 -0.377
HMC 0.3 6.086 2.136 1.210 3.263
HMC 0.5 2.900 46.852 160.247 -0.274
HMC 0.9 13.055 71.206 264.663 -0.220
HMC 0.95 15.535 9.573 12.329 0.484
HMC 0.99 6.053 4.221 5.737 0.319
SMC 0.0 5.440 22.041 46.008 -0.361
SMC 0.3 3.265 2.136 1.210 0.932
SMC 0.5 3.920 46.852 160.247 -0.268
SMC 0.9 21.059 71.206 264.663 -0.189
SMC 0.95 13.786 9.573 12.329 0.342
SMC 0.99 5.761 4.221 5.737 0.268
Metro 0.0 6.485 22.041 46.008 -0.338
Metro 0.3 2.727 2.136 1.210 0.488
Metro 0.5 4.688 46.852 160.247 -0.263
Metro 0.9 13.470 71.206 264.663 -0.218
Metro 0.95 12.430 9.573 12.329 0.232
Metro 0.99 62.909 4.221 5.737 10.229
DEMetro_Z 0.0 4.987 22.041 46.008 -0.371
DEMetro_Z 0.3 4.082 2.136 1.210 1.608
DEMetro_Z 0.5 3.907 46.852 160.247 -0.268
DEMetro_Z 0.9 13.525 71.206 264.663 -0.218
DEMetro_Z 0.95 14.184 9.573 12.329 0.374
DEMetro_Z 0.99 10.041 4.221 5.737 1.014
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.430 0.000162 1.990
HMC 0.3 3.438 0.0037 5.069
HMC 0.5 2.794 0.00943 1.124
HMC 0.9 2.938 0.00654 1.085
HMC 0.95 2.585 0.0194 2.191
HMC 0.99 3.922 0.00126 4.282
SMC 0.0 4.447 0.000297 3.087
SMC 0.3 3.080 0.00794 6.862
SMC 0.5 3.069 0.00636 2.038
SMC 0.9 6.958 3.94e-06 8.146
SMC 0.95 5.970 2.79e-05 9.847
SMC 0.99 5.435 7.54e-05 9.498
Metro 0.0 3.544 0.00237 2.652
Metro 0.3 4.419 0.000468 5.202
Metro 0.5 3.553 0.00137 1.312
Metro 0.9 3.923 0.000534 1.563
Metro 0.95 3.555 0.00301 6.824
Metro 0.99 1.731 0.105 81.691
DEMetro_Z 0.0 5.000 2.78e-05 1.823
DEMetro_Z 0.3 5.932 2.43e-05 6.868
DEMetro_Z 0.5 4.776 5.9e-05 1.558
DEMetro_Z 0.9 4.498 0.000119 1.489
DEMetro_Z 0.95 5.298 6.36e-05 4.662
DEMetro_Z 0.99 3.758 0.00202 7.769
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 1.157 0.267 0.299
Metro_vs_DEMetro_Z 0.3 -0.898 0.385 -0.232
Metro_vs_DEMetro_Z 0.5 -0.780 0.448 -0.201
Metro_vs_DEMetro_Z 0.9 0.188 0.854 0.048
Metro_vs_DEMetro_Z 0.95 1.113 0.284 0.287
Metro_vs_DEMetro_Z 0.99 1.563 0.14 0.404
DEMetro_Z_vs_SMC 0.0 -1.717 0.108 -0.443
DEMetro_Z_vs_SMC 0.3 0.003 0.998 0.001
DEMetro_Z_vs_SMC 0.5 -0.777 0.45 -0.201
DEMetro_Z_vs_SMC 0.9 -6.281 2.02e-05 -1.622
DEMetro_Z_vs_SMC 0.95 -2.953 0.0105 -0.762
DEMetro_Z_vs_SMC 0.99 -0.530 0.604 -0.137
HMC_vs_DEMetro_Z 0.0 0.343 0.737 0.089
HMC_vs_DEMetro_Z 0.3 -0.977 0.345 -0.252
HMC_vs_DEMetro_Z 0.5 -1.175 0.26 -0.303
HMC_vs_DEMetro_Z 0.9 -1.079 0.299 -0.279
HMC_vs_DEMetro_Z 0.95 -2.205 0.0447 -0.569
HMC_vs_DEMetro_Z 0.99 -1.812 0.0916 -0.468
HMC_vs_Metro 0.0 -0.819 0.427 -0.211
HMC_vs_Metro 0.3 -0.091 0.929 -0.023
HMC_vs_Metro 0.5 -0.603 0.556 -0.156
HMC_vs_Metro 0.9 -1.381 0.189 -0.357
HMC_vs_Metro 0.95 -2.636 0.0196 -0.681
HMC_vs_Metro 0.99 -1.659 0.119 -0.428
HMC_vs_SMC 0.0 -1.294 0.217 -0.334
HMC_vs_SMC 0.3 -0.692 0.5 -0.179
HMC_vs_SMC 0.5 -1.746 0.103 -0.451
HMC_vs_SMC 0.9 -5.805 4.56e-05 -1.499
HMC_vs_SMC 0.95 -7.121 5.16e-06 -1.839
HMC_vs_SMC 0.99 -2.402 0.0308 -0.620
Metro_vs_SMC 0.0 -0.590 0.565 -0.152
Metro_vs_SMC 0.3 -0.678 0.509 -0.175
Metro_vs_SMC 0.5 -1.112 0.285 -0.287
Metro_vs_SMC 0.9 -5.518 7.57e-05 -1.425
Metro_vs_SMC 0.95 -1.413 0.18 -0.365
Metro_vs_SMC 0.99 1.516 0.152 0.391
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.290 0.148 0.071 1.990
HMC 0.3 0.276 0.136 0.028 5.069
HMC 0.5 0.257 0.160 0.087 1.124
HMC 0.9 0.267 0.144 0.113 1.085
HMC 0.95 0.218 0.135 0.038 2.191
HMC 0.99 0.222 0.098 0.029 4.282
SMC 0.0 0.369 0.148 0.071 3.087
SMC 0.3 0.325 0.136 0.028 6.862
SMC 0.5 0.336 0.160 0.087 2.038
SMC 0.9 1.066 0.144 0.113 8.146
SMC 0.95 0.508 0.135 0.038 9.847
SMC 0.99 0.373 0.098 0.029 9.498
Metro 0.0 0.338 0.148 0.071 2.652
Metro 0.3 0.280 0.136 0.028 5.202
Metro 0.5 0.274 0.160 0.087 1.312
Metro 0.9 0.321 0.144 0.113 1.563
Metro 0.95 0.394 0.135 0.038 6.824
Metro 0.99 2.459 0.098 0.029 81.691
DEMetro_Z 0.0 0.278 0.148 0.071 1.823
DEMetro_Z 0.3 0.325 0.136 0.028 6.868
DEMetro_Z 0.5 0.295 0.160 0.087 1.558
DEMetro_Z 0.9 0.313 0.144 0.113 1.489
DEMetro_Z 0.95 0.312 0.135 0.038 4.662
DEMetro_Z 0.99 0.323 0.098 0.029 7.769
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.851 0.000186 5.198
HMC 0.3 4.496 0.000346 4.112
HMC 0.5 4.010 0.00106 4.480
HMC 0.9 4.560 0.000384 6.811
HMC 0.95 3.845 0.0013 3.181
HMC 0.99 3.751 0.00198 6.107
SMC 0.0 4.542 0.000397 6.722
SMC 0.3 2.423 0.0293 6.608
SMC 0.5 2.952 0.0102 5.786
SMC 0.9 7.123 5.08e-06 53.260
SMC 0.95 7.712 1.9e-06 22.899
SMC 0.99 7.183 4.34e-06 22.632
Metro 0.0 5.061 8.14e-05 3.660
Metro 0.3 2.758 0.0144 3.325
Metro 0.5 2.808 0.0118 2.118
Metro 0.9 6.823 6.02e-06 10.118
Metro 0.95 5.479 7.01e-05 9.847
Metro 0.99 3.560 0.00313 30.496
DEMetro_Z 0.0 5.245 5.61e-05 3.851
DEMetro_Z 0.3 4.604 0.000318 5.277
DEMetro_Z 0.5 5.638 2.16e-05 3.875
DEMetro_Z 0.9 6.442 1.05e-05 8.241
DEMetro_Z 0.95 5.793 3.51e-05 7.925
DEMetro_Z 0.99 6.516 1.04e-05 10.102
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 -1.610 0.13 -0.416
DEMetro_Z_vs_SMC 0.3 -0.539 0.598 -0.139
DEMetro_Z_vs_SMC 0.5 -1.000 0.334 -0.258
DEMetro_Z_vs_SMC 0.9 -6.124 2.63e-05 -1.581
DEMetro_Z_vs_SMC 0.95 -4.581 0.000428 -1.183
DEMetro_Z_vs_SMC 0.99 -3.114 0.00762 -0.804
HMC_vs_Metro 0.0 1.277 0.222 0.330
HMC_vs_Metro 0.3 0.548 0.593 0.141
HMC_vs_Metro 0.5 1.616 0.128 0.417
HMC_vs_Metro 0.9 -1.530 0.148 -0.395
HMC_vs_Metro 0.95 -3.565 0.0031 -0.921
HMC_vs_Metro 0.99 -3.166 0.00687 -0.817
Metro_vs_DEMetro_Z 0.0 -0.173 0.865 -0.045
Metro_vs_DEMetro_Z 0.3 -1.076 0.3 -0.278
Metro_vs_DEMetro_Z 0.5 -2.149 0.0496 -0.555
Metro_vs_DEMetro_Z 0.9 0.839 0.416 0.217
Metro_vs_DEMetro_Z 0.95 0.750 0.466 0.194
Metro_vs_DEMetro_Z 0.99 2.386 0.0317 0.616
HMC_vs_SMC 0.0 -0.768 0.455 -0.198
HMC_vs_SMC 0.3 -0.811 0.431 -0.209
HMC_vs_SMC 0.5 -0.743 0.47 -0.192
HMC_vs_SMC 0.9 -5.630 6.2e-05 -1.454
HMC_vs_SMC 0.95 -6.903 7.29e-06 -1.782
HMC_vs_SMC 0.99 -4.365 0.000647 -1.127
Metro_vs_SMC 0.0 -2.027 0.0621 -0.523
Metro_vs_SMC 0.3 -1.125 0.28 -0.290
Metro_vs_SMC 0.5 -1.704 0.11 -0.440
Metro_vs_SMC 0.9 -5.353 0.000102 -1.382
Metro_vs_SMC 0.95 -4.412 0.000591 -1.139
Metro_vs_SMC 0.99 0.787 0.445 0.203
HMC_vs_DEMetro_Z 0.0 1.004 0.333 0.259
HMC_vs_DEMetro_Z 0.3 -0.823 0.424 -0.212
HMC_vs_DEMetro_Z 0.5 0.486 0.634 0.126
HMC_vs_DEMetro_Z 0.9 -0.655 0.523 -0.169
HMC_vs_DEMetro_Z 0.95 -3.079 0.00817 -0.795
HMC_vs_DEMetro_Z 0.99 -2.386 0.0317 -0.616
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.037 0.010 0.005 5.198
HMC 0.3 0.034 0.014 0.005 4.112
HMC 0.5 0.040 0.013 0.006 4.480
HMC 0.9 0.039 0.014 0.004 6.811
HMC 0.95 0.028 0.014 0.004 3.181
HMC 0.99 0.033 0.012 0.003 6.107
SMC 0.0 0.045 0.010 0.005 6.722
SMC 0.3 0.046 0.014 0.005 6.608
SMC 0.5 0.048 0.013 0.006 5.786
SMC 0.9 0.212 0.014 0.004 53.260
SMC 0.95 0.115 0.014 0.004 22.899
SMC 0.99 0.091 0.012 0.003 22.632
Metro 0.0 0.029 0.010 0.005 3.660
Metro 0.3 0.030 0.014 0.005 3.325
Metro 0.5 0.026 0.013 0.006 2.118
Metro 0.9 0.051 0.014 0.004 10.118
Metro 0.95 0.058 0.014 0.004 9.847
Metro 0.99 0.118 0.012 0.003 30.496
DEMetro_Z 0.0 0.030 0.010 0.005 3.851
DEMetro_Z 0.3 0.039 0.014 0.005 5.277
DEMetro_Z 0.5 0.036 0.013 0.006 3.875
DEMetro_Z 0.9 0.044 0.014 0.004 8.241
DEMetro_Z 0.95 0.049 0.014 0.004 7.925
DEMetro_Z 0.99 0.047 0.012 0.003 10.102
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
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three_attr_dim

▼

Vary_Dimension_with_Corr_and_Tails (MvStudentT, dimension, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.450 0.0214 1.066
HMC 3 1.360 0.185 0.563
HMC 5 1.165 0.255 0.509
HMC 8 2.402 0.0299 3.672
HMC 15 4.483 0.000313 3.523
HMC 30 2.125 0.0518 10.644
SMC 2 -0.688 0.498 -0.216
SMC 3 1.226 0.232 0.562
SMC 5 3.258 0.00502 3.460
SMC 8 5.123 0.000149 16.597
SMC 15 4.401 0.00059 16.427
SMC 30 6.629 8.29e-06 9.662
Metro 2 4.329 0.000491 3.962
Metro 3 4.375 0.000598 9.901
Metro 5 2.441 0.0285 42.496
Metro 8 4.513 0.000486 77.361
Metro 15 3.312 0.00514 184.394
Metro 30 4.154 0.000974 3891.972
DEMetro_Z 2 2.063 0.0576 4.500
DEMetro_Z 3 2.536 0.0238 41.438
DEMetro_Z 5 5.764 4.9e-05 250.375
DEMetro_Z 8 4.585 0.000424 572.356
DEMetro_Z 15 9.565 1.62e-07 617.535
DEMetro_Z 30 6.918 7.12e-06 3297.933
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.667 0.118 -0.430
HMC_vs_DEMetro_Z 1 -2.498 0.0256 -0.645
HMC_vs_DEMetro_Z 2 -5.750 5.02e-05 -1.485
HMC_vs_DEMetro_Z 3 -4.563 0.000443 -1.178
HMC_vs_DEMetro_Z 4 -9.530 1.69e-07 -2.461
HMC_vs_DEMetro_Z 5 -6.868 7.71e-06 -1.773
Metro_vs_SMC 0 4.592 0.000419 1.186
Metro_vs_SMC 1 4.275 0.000769 1.104
Metro_vs_SMC 2 2.213 0.044 0.571
Metro_vs_SMC 3 3.465 0.00379 0.895
Metro_vs_SMC 4 2.957 0.0104 0.763
Metro_vs_SMC 5 4.142 0.000997 1.069
Metro_vs_DEMetro_Z 0 -0.210 0.837 -0.054
Metro_vs_DEMetro_Z 1 -1.864 0.0834 -0.481
Metro_vs_DEMetro_Z 2 -5.240 0.000125 -1.353
Metro_vs_DEMetro_Z 3 -4.222 0.000854 -1.090
Metro_vs_DEMetro_Z 4 -5.189 0.000137 -1.340
Metro_vs_DEMetro_Z 5 0.562 0.583 0.145
HMC_vs_Metro 0 -2.617 0.0203 -0.676
HMC_vs_Metro 1 -4.037 0.00122 -1.042
HMC_vs_Metro 2 -2.419 0.0298 -0.625
HMC_vs_Metro 3 -4.251 0.000806 -1.098
HMC_vs_Metro 4 -3.234 0.006 -0.835
HMC_vs_Metro 5 -4.135 0.00101 -1.068
HMC_vs_SMC 0 2.992 0.00971 0.772
HMC_vs_SMC 1 0.003 0.998 0.001
HMC_vs_SMC 2 -2.719 0.0166 -0.702
HMC_vs_SMC 3 -3.848 0.00178 -0.993
HMC_vs_SMC 4 -3.700 0.00238 -0.955
HMC_vs_SMC 5 0.190 0.852 0.049
DEMetro_Z_vs_SMC 0 2.117 0.0527 0.546
DEMetro_Z_vs_SMC 1 2.489 0.026 0.643
DEMetro_Z_vs_SMC 2 5.694 5.55e-05 1.470
DEMetro_Z_vs_SMC 3 4.478 0.000521 1.156
DEMetro_Z_vs_SMC 4 9.359 2.11e-07 2.416
DEMetro_Z_vs_SMC 5 6.889 7.45e-06 1.779
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.121 0.069 0.049 1.066
HMC 3 0.073 0.051 0.039 0.563
HMC 5 0.100 0.066 0.066 0.509
HMC 8 0.166 0.059 0.029 3.672
HMC 15 0.173 0.048 0.036 3.523
HMC 30 0.371 0.056 0.030 10.644
SMC 2 0.058 0.069 0.049 -0.216
SMC 3 0.073 0.051 0.039 0.562
SMC 5 0.294 0.066 0.066 3.460
SMC 8 0.542 0.059 0.029 16.597
SMC 15 0.632 0.048 0.036 16.427
SMC 30 0.342 0.056 0.030 9.662
Metro 2 0.264 0.069 0.049 3.962
Metro 3 0.433 0.051 0.039 9.901
Metro 5 2.869 0.066 0.066 42.496
Metro 8 2.309 0.059 0.029 77.361
Metro 15 6.609 0.048 0.036 184.394
Metro 30 115.325 0.056 0.030 3891.972
DEMetro_Z 2 0.290 0.069 0.049 4.500
DEMetro_Z 3 1.650 0.051 0.039 41.438
DEMetro_Z 5 16.580 0.066 0.066 250.375
DEMetro_Z 8 16.701 0.059 0.029 572.356
DEMetro_Z 15 22.021 0.048 0.036 617.535
DEMetro_Z 30 97.731 0.056 0.030 3297.933
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.634 0.532 0.297
HMC 3 0.347 0.731 0.110
HMC 5 -1.025 0.323 -0.265
HMC 8 1.341 0.199 1.391
HMC 15 2.232 0.0368 1.282
HMC 30 1.322 0.197 0.503
SMC 2 0.623 0.539 0.300
SMC 3 2.325 0.0308 1.416
SMC 5 0.148 0.885 0.038
SMC 8 19.459 2.8e-12 22.707
SMC 15 17.700 5.07e-11 82.045
SMC 30 20.790 6.15e-14 15.382
Metro 2 0.748 0.462 0.369
Metro 3 2.419 0.0224 0.927
Metro 5 1.162 0.263 1.748
Metro 8 2.760 0.0152 10.060
Metro 15 2.340 0.0346 128.679
Metro 30 2.629 0.0198 7839.763
DEMetro_Z 2 1.169 0.261 2.808
DEMetro_Z 3 3.214 0.00625 147.616
DEMetro_Z 5 4.915 0.000225 26.859
DEMetro_Z 8 5.712 5.37e-05 282.407
DEMetro_Z 15 6.491 1.42e-05 352.879
DEMetro_Z 30 11.192 2.28e-08 2217.405
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.029 0.977 -0.008
HMC_vs_SMC 1 -2.100 0.0543 -0.542
HMC_vs_SMC 2 -10.619 4.42e-08 -2.742
HMC_vs_SMC 3 -16.036 2.1e-10 -4.140
HMC_vs_SMC 4 -16.942 1.01e-10 -4.374
HMC_vs_SMC 5 -18.347 3.45e-11 -4.737
Metro_vs_DEMetro_Z 0 -1.017 0.326 -0.263
Metro_vs_DEMetro_Z 1 -3.195 0.00649 -0.825
Metro_vs_DEMetro_Z 2 -4.682 0.000353 -1.209
Metro_vs_DEMetro_Z 3 -5.563 6.99e-05 -1.436
Metro_vs_DEMetro_Z 4 -3.046 0.00872 -0.786
Metro_vs_DEMetro_Z 5 1.900 0.0783 0.490
HMC_vs_Metro 0 -1.254 0.23 -0.324
HMC_vs_Metro 1 -2.666 0.0184 -0.688
HMC_vs_Metro 2 -1.358 0.196 -0.351
HMC_vs_Metro 3 -2.223 0.0432 -0.574
HMC_vs_Metro 4 -2.324 0.0357 -0.600
HMC_vs_Metro 5 -2.628 0.0198 -0.679
HMC_vs_DEMetro_Z 0 -1.047 0.313 -0.270
HMC_vs_DEMetro_Z 1 -3.210 0.0063 -0.829
HMC_vs_DEMetro_Z 2 -4.967 0.000207 -1.282
HMC_vs_DEMetro_Z 3 -5.692 5.56e-05 -1.470
HMC_vs_DEMetro_Z 4 -6.462 1.49e-05 -1.668
HMC_vs_DEMetro_Z 5 -11.190 2.28e-08 -2.889
Metro_vs_SMC 0 1.043 0.315 0.269
Metro_vs_SMC 1 -0.803 0.435 -0.207
Metro_vs_SMC 2 1.156 0.267 0.298
Metro_vs_SMC 3 -3.450 0.0039 -0.891
Metro_vs_SMC 4 0.821 0.425 0.212
Metro_vs_SMC 5 2.624 0.02 0.677
DEMetro_Z_vs_SMC 0 1.046 0.313 0.270
DEMetro_Z_vs_SMC 1 3.177 0.00673 0.820
DEMetro_Z_vs_SMC 2 4.906 0.000232 1.267
DEMetro_Z_vs_SMC 3 5.225 0.000129 1.349
DEMetro_Z_vs_SMC 4 5.209 0.000132 1.345
DEMetro_Z_vs_SMC 5 11.123 2.46e-08 2.872
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 8.434 5.161 11.013 0.297
HMC 3 2.527 2.285 2.190 0.110
HMC 5 4.212 38.842 130.805 -0.265
HMC 8 12.087 4.219 5.656 1.391
HMC 15 6.473 2.615 3.008 1.282
HMC 30 12.120 6.295 11.576 0.503
SMC 2 8.461 5.161 11.013 0.300
SMC 3 5.386 2.285 2.190 1.416
SMC 5 43.852 38.842 130.805 0.038
SMC 8 132.657 4.219 5.656 22.707
SMC 15 249.434 2.615 3.008 82.045
SMC 30 184.356 6.295 11.576 15.382
Metro 2 9.229 5.161 11.013 0.369
Metro 3 4.314 2.285 2.190 0.927
Metro 5 267.434 38.842 130.805 1.748
Metro 8 61.121 4.219 5.656 10.060
Metro 15 389.728 2.615 3.008 128.679
Metro 30 90760.224 6.295 11.576 7839.763
DEMetro_Z 2 36.085 5.161 11.013 2.808
DEMetro_Z 3 325.541 2.285 2.190 147.616
DEMetro_Z 5 3552.137 38.842 130.805 26.859
DEMetro_Z 8 1601.587 4.219 5.656 282.407
DEMetro_Z 15 1064.199 2.615 3.008 352.879
DEMetro_Z 30 25675.212 6.295 11.576 2217.405
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.360 0.000264 2.382
HMC 3 4.882 8.81e-05 2.902
HMC 5 2.716 0.0114 0.907
HMC 8 3.423 0.00393 6.593
HMC 15 4.782 0.000275 11.595
HMC 30 4.025 0.00124 18.187
SMC 2 0.666 0.511 0.291
SMC 3 6.940 6.2e-06 18.430
SMC 5 20.473 3.63e-12 36.083
SMC 8 39.335 8.44e-16 191.603
SMC 15 27.505 1.36e-13 413.381
SMC 30 66.436 5.55e-19 335.428
Metro 2 6.598 8.42e-06 9.101
Metro 3 7.176 4.24e-06 18.773
Metro 5 2.557 0.0228 35.093
Metro 8 5.286 0.000115 100.051
Metro 15 4.739 0.000317 326.732
Metro 30 4.937 0.000219 5130.800
DEMetro_Z 2 2.261 0.0401 11.916
DEMetro_Z 3 5.103 0.000161 201.514
DEMetro_Z 5 8.580 6e-07 352.526
DEMetro_Z 8 9.512 1.73e-07 754.513
DEMetro_Z 15 14.032 1.23e-09 1062.374
DEMetro_Z 30 16.775 1.15e-10 5112.701
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.510 0.618 -0.132
Metro_vs_DEMetro_Z 1 -4.679 0.000355 -1.208
Metro_vs_DEMetro_Z 2 -7.584 2.54e-06 -1.958
Metro_vs_DEMetro_Z 3 -8.620 5.68e-07 -2.226
Metro_vs_DEMetro_Z 4 -7.438 3.16e-06 -1.921
Metro_vs_DEMetro_Z 5 0.017 0.987 0.004
DEMetro_Z_vs_SMC 0 2.162 0.0484 0.558
DEMetro_Z_vs_SMC 1 4.534 0.000467 1.171
DEMetro_Z_vs_SMC 2 7.573 2.58e-06 1.955
DEMetro_Z_vs_SMC 3 6.946 6.81e-06 1.793
DEMetro_Z_vs_SMC 4 8.612 5.75e-07 2.224
DEMetro_Z_vs_SMC 5 15.734 2.7e-10 4.062
HMC_vs_DEMetro_Z 0 -1.819 0.0904 -0.470
HMC_vs_DEMetro_Z 1 -5.031 0.000184 -1.299
HMC_vs_DEMetro_Z 2 -8.539 6.36e-07 -2.205
HMC_vs_DEMetro_Z 3 -9.453 1.87e-07 -2.441
HMC_vs_DEMetro_Z 4 -14.013 1.25e-09 -3.618
HMC_vs_DEMetro_Z 5 -16.717 1.2e-10 -4.316
HMC_vs_Metro 0 -4.742 0.000315 -1.224
HMC_vs_Metro 1 -6.242 2.16e-05 -1.612
HMC_vs_Metro 2 -2.489 0.026 -0.643
HMC_vs_Metro 3 -4.844 0.00026 -1.251
HMC_vs_Metro 4 -4.598 0.000414 -1.187
HMC_vs_Metro 5 -4.910 0.00023 -1.268
HMC_vs_SMC 0 3.744 0.00218 0.967
HMC_vs_SMC 1 -5.878 4.02e-05 -1.518
HMC_vs_SMC 2 -19.834 1.2e-11 -5.121
HMC_vs_SMC 3 -35.629 3.87e-15 -9.199
HMC_vs_SMC 4 -27.682 1.26e-13 -7.148
HMC_vs_SMC 5 -47.162 7.87e-17 -12.177
Metro_vs_SMC 0 7.215 4.46e-06 1.863
Metro_vs_SMC 1 0.113 0.912 0.029
Metro_vs_SMC 2 -0.075 0.942 -0.019
Metro_vs_SMC 3 -4.912 0.000229 -1.268
Metro_vs_SMC 4 -1.146 0.271 -0.296
Metro_vs_SMC 5 4.618 0.000399 1.192
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.185 0.111 0.031 2.382
HMC 3 0.165 0.094 0.024 2.902
HMC 5 0.204 0.124 0.088 0.907
HMC 8 0.321 0.104 0.033 6.593
HMC 15 0.373 0.090 0.024 11.595
HMC 30 0.603 0.103 0.027 18.187
SMC 2 0.120 0.111 0.031 0.291
SMC 3 0.541 0.094 0.024 18.430
SMC 5 3.309 0.124 0.088 36.083
SMC 8 6.421 0.104 0.033 191.603
SMC 15 10.200 0.090 0.024 413.381
SMC 30 9.323 0.103 0.027 335.428
Metro 2 0.396 0.111 0.031 9.101
Metro 3 0.549 0.094 0.024 18.773
Metro 5 3.222 0.124 0.088 35.093
Metro 8 3.403 0.104 0.033 100.051
Metro 15 8.080 0.090 0.024 326.732
Metro 30 141.136 0.103 0.027 5130.800
DEMetro_Z 2 0.484 0.111 0.031 11.916
DEMetro_Z 3 4.977 0.094 0.024 201.514
DEMetro_Z 5 31.241 0.124 0.088 352.526
DEMetro_Z 8 24.981 0.104 0.033 754.513
DEMetro_Z 15 26.072 0.090 0.024 1062.374
DEMetro_Z 30 140.638 0.103 0.027 5112.701
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.430 0.00257 1.975
HMC 3 3.968 0.00105 3.619
HMC 5 3.954 0.000842 2.554
HMC 8 5.614 3.55e-05 5.152
HMC 15 5.466 7.94e-05 17.413
HMC 30 6.925 6.71e-06 26.872
SMC 2 0.678 0.504 0.250
SMC 3 10.348 5.04e-08 26.409
SMC 5 38.224 5.41e-16 72.099
SMC 8 59.263 6.1e-19 95.764
SMC 15 88.226 1.88e-21 144.864
SMC 30 54.393 5.67e-18 138.469
Metro 2 6.579 9.9e-06 11.471
Metro 3 7.774 1.79e-06 27.947
Metro 5 9.014 3.18e-07 43.561
Metro 8 14.489 7.49e-10 72.372
Metro 15 14.681 6.63e-10 138.867
Metro 30 35.186 4.23e-15 220.927
DEMetro_Z 2 5.382 8.32e-05 9.406
DEMetro_Z 3 7.743 1.98e-06 71.891
DEMetro_Z 5 56.582 1.52e-18 98.588
DEMetro_Z 8 30.344 2.91e-14 118.503
DEMetro_Z 15 25.933 2.93e-13 182.583
DEMetro_Z 30 26.042 2.76e-13 177.736
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.061 0.000174 1.307
DEMetro_Z_vs_SMC 1 4.337 0.000684 1.120
DEMetro_Z_vs_SMC 2 12.570 5.14e-09 3.246
DEMetro_Z_vs_SMC 3 4.650 0.000375 1.201
DEMetro_Z_vs_SMC 4 4.806 0.000279 1.241
DEMetro_Z_vs_SMC 5 5.309 0.00011 1.371
HMC_vs_Metro 0 -4.977 0.000203 -1.285
HMC_vs_Metro 1 -7.525 2.77e-06 -1.943
HMC_vs_Metro 2 -8.489 6.82e-07 -2.192
HMC_vs_Metro 3 -12.543 5.29e-09 -3.239
HMC_vs_Metro 4 -14.343 9.19e-10 -3.703
HMC_vs_Metro 5 -28.597 8.08e-14 -7.384
Metro_vs_DEMetro_Z 0 0.937 0.365 0.242
Metro_vs_DEMetro_Z 1 -4.483 0.000516 -1.157
Metro_vs_DEMetro_Z 2 -10.065 8.62e-08 -2.599
Metro_vs_DEMetro_Z 3 -6.622 1.15e-05 -1.710
Metro_vs_DEMetro_Z 4 -4.151 0.000979 -1.072
Metro_vs_DEMetro_Z 5 5.424 8.96e-05 1.401
HMC_vs_SMC 0 2.454 0.0278 0.634
HMC_vs_SMC 1 -9.230 2.5e-07 -2.383
HMC_vs_SMC 2 -39.346 9.77e-16 -10.159
HMC_vs_SMC 3 -59.197 3.31e-18 -15.285
HMC_vs_SMC 4 -37.085 2.22e-15 -9.575
HMC_vs_SMC 5 -22.804 1.8e-12 -5.888
Metro_vs_SMC 0 6.397 1.66e-05 1.652
Metro_vs_SMC 1 0.450 0.659 0.116
Metro_vs_SMC 2 -5.392 9.49e-05 -1.392
Metro_vs_SMC 3 -4.580 0.000429 -1.182
Metro_vs_SMC 4 -0.593 0.562 -0.153
Metro_vs_SMC 5 12.245 7.21e-09 3.162
HMC_vs_DEMetro_Z 0 -4.261 0.00079 -1.100
HMC_vs_DEMetro_Z 1 -7.409 3.31e-06 -1.913
HMC_vs_DEMetro_Z 2 -51.144 2.54e-17 -13.205
HMC_vs_DEMetro_Z 3 -26.560 2.23e-13 -6.858
HMC_vs_DEMetro_Z 4 -22.004 2.94e-12 -5.681
HMC_vs_DEMetro_Z 5 -20.166 9.61e-12 -5.207
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.025 0.015 0.005 1.975
HMC 3 0.030 0.015 0.004 3.619
HMC 5 0.031 0.017 0.006 2.554
HMC 8 0.044 0.016 0.005 5.152
HMC 15 0.078 0.014 0.004 17.413
HMC 30 0.102 0.014 0.003 26.872
SMC 2 0.016 0.015 0.005 0.250
SMC 3 0.127 0.015 0.004 26.409
SMC 5 0.438 0.017 0.006 72.099
SMC 8 0.528 0.016 0.005 95.764
SMC 15 0.549 0.014 0.004 144.864
SMC 30 0.468 0.014 0.003 138.469
Metro 2 0.074 0.015 0.005 11.471
Metro 3 0.134 0.015 0.004 27.947
Metro 5 0.271 0.017 0.006 43.561
Metro 8 0.403 0.016 0.005 72.372
Metro 15 0.527 0.014 0.004 138.867
Metro 30 0.739 0.014 0.003 220.927
DEMetro_Z 2 0.064 0.015 0.005 9.406
DEMetro_Z 3 0.321 0.015 0.004 71.891
DEMetro_Z 5 0.592 0.017 0.006 98.588
DEMetro_Z 8 0.650 0.016 0.005 118.503
DEMetro_Z 15 0.688 0.014 0.004 182.583
DEMetro_Z 30 0.597 0.014 0.003 177.736
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.001 0.0575 1.020
HMC 3 2.030 0.0544 1.047
HMC 5 2.065 0.0507 1.067
HMC 8 2.327 0.0324 1.855
HMC 15 2.110 0.0529 4.901
HMC 30 2.357 0.0333 6.929
SMC 2 -0.773 0.447 -0.242
SMC 3 1.425 0.168 0.745
SMC 5 2.647 0.0179 3.031
SMC 8 3.179 0.00662 11.204
SMC 15 5.432 8.19e-05 13.518
SMC 30 5.245 0.000115 12.925
Metro 2 7.480 6.51e-07 5.472
Metro 3 3.355 0.00463 10.039
Metro 5 2.517 0.0245 9.569
Metro 8 2.813 0.0138 117.877
Metro 15 1.611 0.129 401.862
Metro 30 3.807 0.00192 3335.012
DEMetro_Z 2 2.716 0.0112 1.012
DEMetro_Z 3 3.048 0.00864 16.413
DEMetro_Z 5 4.104 0.00107 55.651
DEMetro_Z 8 5.439 8.72e-05 264.699
DEMetro_Z 15 5.379 9.72e-05 842.426
DEMetro_Z 30 4.745 0.000314 4363.670
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.013 0.99 0.003
HMC_vs_DEMetro_Z 1 -2.831 0.0133 -0.731
HMC_vs_DEMetro_Z 2 -4.004 0.00131 -1.034
HMC_vs_DEMetro_Z 3 -5.391 9.52e-05 -1.392
HMC_vs_DEMetro_Z 4 -5.343 0.000104 -1.380
HMC_vs_DEMetro_Z 5 -4.740 0.000316 -1.224
Metro_vs_SMC 0 8.351 8.27e-07 2.156
Metro_vs_SMC 1 3.139 0.00724 0.811
Metro_vs_SMC 2 2.258 0.0405 0.583
Metro_vs_SMC 3 2.508 0.0251 0.648
Metro_vs_SMC 4 1.554 0.142 0.401
Metro_vs_SMC 5 3.791 0.00199 0.979
Metro_vs_DEMetro_Z 0 5.895 3.9e-05 1.522
Metro_vs_DEMetro_Z 1 -1.398 0.184 -0.361
Metro_vs_DEMetro_Z 2 -3.448 0.00392 -0.890
Metro_vs_DEMetro_Z 3 -2.236 0.0422 -0.577
Metro_vs_DEMetro_Z 4 -1.287 0.219 -0.332
Metro_vs_DEMetro_Z 5 -0.797 0.439 -0.206
HMC_vs_Metro 0 -5.684 5.65e-05 -1.468
HMC_vs_Metro 1 -2.835 0.0132 -0.732
HMC_vs_Metro 2 -2.248 0.0412 -0.581
HMC_vs_Metro 3 -2.754 0.0155 -0.711
HMC_vs_Metro 4 -1.594 0.133 -0.412
HMC_vs_Metro 5 -3.799 0.00195 -0.981
HMC_vs_SMC 0 2.656 0.0188 0.686
HMC_vs_SMC 1 0.467 0.648 0.120
HMC_vs_SMC 2 -1.585 0.135 -0.409
HMC_vs_SMC 3 -2.704 0.0171 -0.698
HMC_vs_SMC 4 -2.732 0.0162 -0.705
HMC_vs_SMC 5 -1.816 0.0909 -0.469
DEMetro_Z_vs_SMC 0 4.205 0.000881 1.086
DEMetro_Z_vs_SMC 1 2.909 0.0114 0.751
DEMetro_Z_vs_SMC 2 3.883 0.00166 1.003
DEMetro_Z_vs_SMC 3 5.068 0.000172 1.308
DEMetro_Z_vs_SMC 4 5.328 0.000107 1.376
DEMetro_Z_vs_SMC 5 4.736 0.000319 1.223
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.119 0.069 0.049 1.020
HMC 3 0.092 0.051 0.039 1.047
HMC 5 0.137 0.066 0.066 1.067
HMC 8 0.113 0.059 0.029 1.855
HMC 15 0.222 0.048 0.036 4.901
HMC 30 0.261 0.056 0.030 6.929
SMC 2 0.057 0.069 0.049 -0.242
SMC 3 0.080 0.051 0.039 0.745
SMC 5 0.266 0.066 0.066 3.031
SMC 8 0.385 0.059 0.029 11.204
SMC 15 0.529 0.048 0.036 13.518
SMC 30 0.438 0.056 0.030 12.925
Metro 2 0.338 0.069 0.049 5.472
Metro 3 0.439 0.051 0.039 10.039
Metro 5 0.697 0.066 0.066 9.569
Metro 8 3.487 0.059 0.029 117.877
Metro 15 14.347 0.048 0.036 401.862
Metro 30 98.829 0.056 0.030 3335.012
DEMetro_Z 2 0.119 0.069 0.049 1.012
DEMetro_Z 3 0.685 0.051 0.039 16.413
DEMetro_Z 5 3.737 0.066 0.066 55.651
DEMetro_Z 8 7.756 0.059 0.029 264.699
DEMetro_Z 15 30.024 0.048 0.036 842.426
DEMetro_Z 30 129.295 0.056 0.030 4363.670
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.597 0.556 0.295
HMC 3 1.224 0.232 0.509
HMC 5 -0.987 0.34 -0.255
HMC 8 -0.477 0.64 -0.129
HMC 15 1.437 0.172 2.920
HMC 30 0.990 0.331 0.333
SMC 2 0.593 0.559 0.284
SMC 3 0.810 0.427 0.423
SMC 5 -0.178 0.861 -0.046
SMC 8 7.098 4.84e-06 19.190
SMC 15 19.449 1.46e-11 106.611
SMC 30 13.083 2.21e-09 29.239
Metro 2 0.802 0.43 0.381
Metro 3 1.225 0.233 0.630
Metro 5 -0.961 0.353 -0.248
Metro 8 1.102 0.289 22.993
Metro 15 1.062 0.306 622.557
Metro 30 1.501 0.156 2688.050
DEMetro_Z 2 0.832 0.414 0.402
DEMetro_Z 3 1.998 0.0655 59.253
DEMetro_Z 5 2.495 0.0246 3.257
DEMetro_Z 8 3.109 0.00769 93.470
DEMetro_Z 15 3.631 0.00272 75.266
DEMetro_Z 30 7.862 1.68e-06 576.404
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.257 0.801 0.066
HMC_vs_SMC 1 0.159 0.876 0.041
HMC_vs_SMC 2 -6.703 1.01e-05 -1.731
HMC_vs_SMC 3 -7.139 5.02e-06 -1.843
HMC_vs_SMC 4 -16.814 1.11e-10 -4.341
HMC_vs_SMC 5 -13.205 2.71e-09 -3.409
Metro_vs_DEMetro_Z 0 -0.290 0.776 -0.075
Metro_vs_DEMetro_Z 1 -1.985 0.0671 -0.513
Metro_vs_DEMetro_Z 2 -2.754 0.0155 -0.711
Metro_vs_DEMetro_Z 3 -1.793 0.0945 -0.463
Metro_vs_DEMetro_Z 4 0.942 0.362 0.243
Metro_vs_DEMetro_Z 5 1.170 0.262 0.302
HMC_vs_Metro 0 -0.937 0.364 -0.242
HMC_vs_Metro 1 -0.248 0.807 -0.064
HMC_vs_Metro 2 -0.362 0.723 -0.093
HMC_vs_Metro 3 -1.110 0.286 -0.287
HMC_vs_Metro 4 -1.057 0.308 -0.273
HMC_vs_Metro 5 -1.500 0.156 -0.387
HMC_vs_DEMetro_Z 0 -1.726 0.106 -0.446
HMC_vs_DEMetro_Z 1 -1.987 0.0669 -0.513
HMC_vs_DEMetro_Z 2 -2.746 0.0158 -0.709
HMC_vs_DEMetro_Z 3 -3.115 0.0076 -0.804
HMC_vs_DEMetro_Z 4 -3.630 0.00273 -0.937
HMC_vs_DEMetro_Z 5 -7.854 1.7e-06 -2.028
Metro_vs_SMC 0 0.998 0.335 0.258
Metro_vs_SMC 1 0.319 0.755 0.082
Metro_vs_SMC 2 -7.555 2.65e-06 -1.951
Metro_vs_SMC 3 0.184 0.857 0.048
Metro_vs_SMC 4 0.879 0.394 0.227
Metro_vs_SMC 5 1.483 0.16 0.383
DEMetro_Z_vs_SMC 0 1.990 0.0664 0.514
DEMetro_Z_vs_SMC 1 1.979 0.0678 0.511
DEMetro_Z_vs_SMC 2 2.572 0.0222 0.664
DEMetro_Z_vs_SMC 3 2.518 0.0246 0.650
DEMetro_Z_vs_SMC 4 -1.437 0.173 -0.371
DEMetro_Z_vs_SMC 5 7.401 3.35e-06 1.911
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 8.405 5.161 11.013 0.295
HMC 3 3.399 2.285 2.190 0.509
HMC 5 5.468 38.842 130.805 -0.255
HMC 8 3.491 4.219 5.656 -0.129
HMC 15 11.400 2.615 3.008 2.920
HMC 30 10.154 6.295 11.576 0.333
SMC 2 8.292 5.161 11.013 0.284
SMC 3 3.212 2.285 2.190 0.423
SMC 5 32.783 38.842 130.805 -0.046
SMC 8 112.760 4.219 5.656 19.190
SMC 15 323.337 2.615 3.008 106.611
SMC 30 344.772 6.295 11.576 29.239
Metro 2 9.354 5.161 11.013 0.381
Metro 3 3.665 2.285 2.190 0.630
Metro 5 6.343 38.842 130.805 -0.248
Metro 8 134.275 4.219 5.656 22.993
Metro 15 1875.488 2.615 3.008 622.557
Metro 30 31123.445 6.295 11.576 2688.050
DEMetro_Z 2 9.588 5.161 11.013 0.402
DEMetro_Z 3 132.040 2.285 2.190 59.253
DEMetro_Z 5 464.850 38.842 130.805 3.257
DEMetro_Z 8 532.911 4.219 5.656 93.470
DEMetro_Z 15 229.042 2.615 3.008 75.266
DEMetro_Z 30 6678.804 6.295 11.576 576.404
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.277 0.000345 2.453
HMC 3 4.296 0.000354 2.599
HMC 5 2.902 0.00762 1.306
HMC 8 5.092 4.88e-05 2.878
HMC 15 4.219 0.000817 10.081
HMC 30 4.781 0.000274 11.257
SMC 2 1.070 0.296 0.537
SMC 3 3.545 0.00317 10.928
SMC 5 13.512 1.36e-09 27.866
SMC 8 11.222 2.19e-08 178.823
SMC 15 37.826 1.65e-15 466.811
SMC 30 27.956 1.09e-13 452.052
Metro 2 8.914 1.93e-07 11.069
Metro 3 5.487 7.66e-05 17.944
Metro 5 3.812 0.00183 9.133
Metro 8 2.725 0.0164 99.330
Metro 15 1.680 0.115 535.409
Metro 30 3.915 0.00156 3211.924
DEMetro_Z 2 7.320 2.5e-07 3.867
DEMetro_Z 3 2.830 0.0134 62.814
DEMetro_Z 5 4.737 0.000318 74.075
DEMetro_Z 8 6.843 8.02e-06 369.084
DEMetro_Z 15 6.020 3.14e-05 1100.073
DEMetro_Z 30 6.181 2.39e-05 4450.883
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 5.893 3.91e-05 1.522
Metro_vs_DEMetro_Z 1 -2.069 0.0575 -0.534
Metro_vs_DEMetro_Z 2 -4.191 0.000906 -1.082
Metro_vs_DEMetro_Z 3 -4.454 0.000546 -1.150
Metro_vs_DEMetro_Z 4 -1.433 0.174 -0.370
Metro_vs_DEMetro_Z 5 -1.059 0.307 -0.274
DEMetro_Z_vs_SMC 0 6.087 2.8e-05 1.572
DEMetro_Z_vs_SMC 1 2.220 0.0435 0.573
DEMetro_Z_vs_SMC 2 2.827 0.0134 0.730
DEMetro_Z_vs_SMC 3 3.603 0.00288 0.930
DEMetro_Z_vs_SMC 4 3.456 0.00386 0.892
DEMetro_Z_vs_SMC 5 5.530 7.41e-05 1.428
HMC_vs_DEMetro_Z 0 -2.407 0.0305 -0.621
HMC_vs_DEMetro_Z 1 -2.725 0.0164 -0.704
HMC_vs_DEMetro_Z 2 -4.644 0.000379 -1.199
HMC_vs_DEMetro_Z 3 -6.774 8.96e-06 -1.749
HMC_vs_DEMetro_Z 4 -5.971 3.42e-05 -1.542
HMC_vs_DEMetro_Z 5 -6.167 2.45e-05 -1.592
HMC_vs_Metro 0 -6.502 1.4e-05 -1.679
HMC_vs_Metro 1 -4.579 0.000429 -1.182
HMC_vs_Metro 2 -3.160 0.00695 -0.816
HMC_vs_Metro 3 -2.639 0.0194 -0.681
HMC_vs_Metro 4 -1.649 0.121 -0.426
HMC_vs_Metro 5 -3.898 0.00161 -1.007
HMC_vs_SMC 0 6.829 8.2e-06 1.763
HMC_vs_SMC 1 -2.646 0.0192 -0.683
HMC_vs_SMC 2 -12.236 7.28e-09 -3.159
HMC_vs_SMC 3 -11.090 2.56e-08 -2.863
HMC_vs_SMC 4 -35.344 4.32e-15 -9.126
HMC_vs_SMC 5 -28.363 9.04e-14 -7.323
Metro_vs_SMC 0 9.125 2.87e-07 2.356
Metro_vs_SMC 1 1.990 0.0665 0.514
Metro_vs_SMC 2 -6.828 8.22e-06 -1.763
Metro_vs_SMC 3 -2.282 0.0386 -0.589
Metro_vs_SMC 4 0.214 0.834 0.055
Metro_vs_SMC 5 3.351 0.00476 0.865
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.187 0.111 0.031 2.453
HMC 3 0.157 0.094 0.024 2.599
HMC 5 0.239 0.124 0.088 1.306
HMC 8 0.199 0.104 0.033 2.878
HMC 15 0.336 0.090 0.024 10.081
HMC 30 0.413 0.103 0.027 11.257
SMC 2 0.127 0.111 0.031 0.537
SMC 3 0.359 0.094 0.024 10.928
SMC 5 2.584 0.124 0.088 27.866
SMC 8 6.000 0.104 0.033 178.823
SMC 15 11.506 0.090 0.024 466.811
SMC 30 12.529 0.103 0.027 452.052
Metro 2 0.457 0.111 0.031 11.069
Metro 3 0.529 0.094 0.024 17.944
Metro 5 0.930 0.124 0.088 9.133
Metro 8 3.379 0.104 0.033 99.330
Metro 15 13.184 0.090 0.024 535.409
Metro 30 88.391 0.103 0.027 3211.924
DEMetro_Z 2 0.232 0.111 0.031 3.867
DEMetro_Z 3 1.616 0.094 0.024 62.814
DEMetro_Z 5 6.663 0.124 0.088 74.075
DEMetro_Z 8 12.273 0.104 0.033 369.084
DEMetro_Z 15 26.994 0.090 0.024 1100.073
DEMetro_Z 30 122.447 0.103 0.027 4450.883
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.582 0.018 1.610
HMC 3 4.055 0.000645 2.533
HMC 5 4.958 5.57e-05 2.563
HMC 8 5.798 2.23e-05 4.923
HMC 15 7.618 1.69e-06 11.635
HMC 30 6.272 1.83e-05 14.643
SMC 2 1.124 0.274 0.661
SMC 3 4.605 0.000399 17.413
SMC 5 36.178 1.09e-15 65.153
SMC 8 26.428 1.93e-13 95.622
SMC 15 65.876 3.39e-19 158.048
SMC 30 67.474 2.35e-19 159.429
Metro 2 7.796 1.46e-06 14.933
Metro 3 12.136 4.82e-09 20.677
Metro 5 5.773 4.76e-05 36.419
Metro 8 8.070 1.22e-06 76.408
Metro 15 13.089 3.01e-09 161.946
Metro 30 23.564 1.13e-12 257.588
DEMetro_Z 2 6.436 2.63e-06 3.796
DEMetro_Z 3 4.197 0.000888 24.794
DEMetro_Z 5 13.689 1.58e-09 67.795
DEMetro_Z 8 17.896 4.59e-11 116.029
DEMetro_Z 15 21.599 3.72e-12 257.751
DEMetro_Z 30 18.574 2.89e-11 246.682
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.764 0.0021 0.972
DEMetro_Z_vs_SMC 1 0.973 0.347 0.251
DEMetro_Z_vs_SMC 2 0.420 0.681 0.109
DEMetro_Z_vs_SMC 3 2.655 0.0188 0.686
DEMetro_Z_vs_SMC 4 7.649 2.3e-06 1.975
DEMetro_Z_vs_SMC 5 6.397 1.66e-05 1.652
HMC_vs_Metro 0 -6.950 6.76e-06 -1.795
HMC_vs_Metro 1 -11.038 2.71e-08 -2.850
HMC_vs_Metro 2 -5.446 8.62e-05 -1.406
HMC_vs_Metro 3 -7.552 2.66e-06 -1.950
HMC_vs_Metro 4 -12.438 5.89e-09 -3.212
HMC_vs_Metro 5 -21.579 3.83e-12 -5.572
Metro_vs_DEMetro_Z 0 5.526 7.47e-05 1.427
Metro_vs_DEMetro_Z 1 -0.675 0.511 -0.174
Metro_vs_DEMetro_Z 2 -3.573 0.00306 -0.923
Metro_vs_DEMetro_Z 3 -3.451 0.0039 -0.891
Metro_vs_DEMetro_Z 4 -5.057 0.000175 -1.306
Metro_vs_DEMetro_Z 5 0.685 0.504 0.177
HMC_vs_SMC 0 1.055 0.309 0.272
HMC_vs_SMC 1 -3.870 0.0017 -0.999
HMC_vs_SMC 2 -32.991 1.12e-14 -8.518
HMC_vs_SMC 3 -23.659 1.09e-12 -6.109
HMC_vs_SMC 4 -59.439 3.13e-18 -15.347
HMC_vs_SMC 5 -47.242 7.68e-17 -12.198
Metro_vs_SMC 0 6.709 9.96e-06 1.732
Metro_vs_SMC 1 0.824 0.424 0.213
Metro_vs_SMC 2 -4.360 0.000653 -1.126
Metro_vs_SMC 3 -2.130 0.0514 -0.550
Metro_vs_SMC 4 0.334 0.743 0.086
Metro_vs_SMC 5 9.546 1.66e-07 2.465
HMC_vs_DEMetro_Z 0 -3.383 0.00446 -0.873
HMC_vs_DEMetro_Z 1 -3.804 0.00194 -0.982
HMC_vs_DEMetro_Z 2 -13.076 3.08e-09 -3.376
HMC_vs_DEMetro_Z 3 -16.444 1.5e-10 -4.246
HMC_vs_DEMetro_Z 4 -20.190 9.46e-12 -5.213
HMC_vs_DEMetro_Z 5 -16.476 1.46e-10 -4.254
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.023 0.015 0.005 1.610
HMC 3 0.026 0.015 0.004 2.533
HMC 5 0.032 0.017 0.006 2.563
HMC 8 0.043 0.016 0.005 4.923
HMC 15 0.057 0.014 0.004 11.635
HMC 30 0.062 0.014 0.003 14.643
SMC 2 0.018 0.015 0.005 0.661
SMC 3 0.089 0.015 0.004 17.413
SMC 5 0.397 0.017 0.006 65.153
SMC 8 0.527 0.016 0.005 95.622
SMC 15 0.597 0.014 0.004 158.048
SMC 30 0.537 0.014 0.003 159.429
Metro 2 0.092 0.015 0.005 14.933
Metro 3 0.103 0.015 0.004 20.677
Metro 5 0.229 0.017 0.006 36.419
Metro 8 0.425 0.016 0.005 76.408
Metro 15 0.612 0.014 0.004 161.946
Metro 30 0.860 0.014 0.003 257.588
DEMetro_Z 2 0.034 0.015 0.005 3.796
DEMetro_Z 3 0.121 0.015 0.004 24.794
DEMetro_Z 5 0.413 0.017 0.006 67.795
DEMetro_Z 8 0.637 0.016 0.005 116.029
DEMetro_Z 15 0.965 0.014 0.004 257.751
DEMetro_Z 30 0.824 0.014 0.003 246.682
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

Vary_Dimension_with_Corr_and_MM (Mixture, dimension, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.644 1.08e-05 35.516
HMC 3 5.614 5.89e-05 13.951
HMC 5 5.717 4.64e-05 11.086
HMC 8 4.563 0.000385 7.013
HMC 15 2.966 0.0098 5.042
HMC 30 4.336 0.000638 8.863
SMC 2 -0.328 0.746 -0.147
SMC 3 -1.410 0.173 -0.413
SMC 5 -1.902 0.0724 -0.535
SMC 8 0.194 0.848 0.068
SMC 15 0.608 0.548 0.221
SMC 30 -0.866 0.395 -0.265
Metro 2 5.658 5.07e-05 10.304
Metro 3 4.748 0.000263 6.874
Metro 5 5.150 0.000142 17.697
Metro 8 7.911 1.4e-06 22.483
Metro 15 6.712 8.9e-06 16.946
Metro 30 6.194 2.31e-05 47.963
DEMetro_Z 2 4.180 0.000914 18.590
DEMetro_Z 3 3.801 0.00194 50.143
DEMetro_Z 5 6.228 2.21e-05 241.484
DEMetro_Z 8 12.135 8.09e-09 401.153
DEMetro_Z 15 18.008 4.42e-11 451.586
DEMetro_Z 30 30.364 3.5e-14 566.333
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 2.888 0.0119 0.746
HMC_vs_DEMetro_Z 1 -2.614 0.0204 -0.675
HMC_vs_DEMetro_Z 2 -5.971 3.42e-05 -1.542
HMC_vs_DEMetro_Z 3 -11.993 9.43e-09 -3.096
HMC_vs_DEMetro_Z 4 -17.551 6.27e-11 -4.532
HMC_vs_DEMetro_Z 5 -29.956 4.26e-14 -7.735
Metro_vs_SMC 0 5.447 8.6e-05 1.406
Metro_vs_SMC 1 5.144 0.000149 1.328
Metro_vs_SMC 2 5.252 0.000122 1.356
Metro_vs_SMC 3 7.785 1.88e-06 2.010
Metro_vs_SMC 4 6.534 1.33e-05 1.687
Metro_vs_SMC 5 6.250 2.13e-05 1.614
Metro_vs_DEMetro_Z 0 -1.760 0.1 -0.454
Metro_vs_DEMetro_Z 1 -3.267 0.00562 -0.844
Metro_vs_DEMetro_Z 2 -5.627 6.24e-05 -1.453
Metro_vs_DEMetro_Z 3 -11.233 2.17e-08 -2.900
Metro_vs_DEMetro_Z 4 -17.312 7.53e-11 -4.470
Metro_vs_DEMetro_Z 5 -30.333 3.58e-14 -7.832
HMC_vs_Metro 0 4.152 0.000978 1.072
HMC_vs_Metro 1 2.144 0.05 0.554
HMC_vs_Metro 2 -1.553 0.143 -0.401
HMC_vs_Metro 3 -4.773 0.000297 -1.232
HMC_vs_Metro 4 -3.688 0.00243 -0.952
HMC_vs_Metro 5 -4.962 0.000209 -1.281
HMC_vs_SMC 0 6.681 1.04e-05 1.725
HMC_vs_SMC 1 5.844 4.26e-05 1.509
HMC_vs_SMC 2 6.071 2.88e-05 1.568
HMC_vs_SMC 3 4.575 0.000432 1.181
HMC_vs_SMC 4 2.742 0.0159 0.708
HMC_vs_SMC 5 4.570 0.000437 1.180
DEMetro_Z_vs_SMC 0 4.156 0.00097 1.073
DEMetro_Z_vs_SMC 1 3.820 0.00187 0.986
DEMetro_Z_vs_SMC 2 6.249 2.13e-05 1.613
DEMetro_Z_vs_SMC 3 12.089 8.5e-09 3.121
DEMetro_Z_vs_SMC 4 18.062 4.26e-11 4.664
DEMetro_Z_vs_SMC 5 30.531 3.27e-14 7.883
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.375 0.025 0.010 35.516
HMC 3 0.273 0.027 0.018 13.951
HMC 5 0.182 0.024 0.014 11.086
HMC 8 0.111 0.022 0.013 7.013
HMC 15 0.082 0.019 0.013 5.042
HMC 30 0.122 0.019 0.012 8.863
SMC 2 0.024 0.025 0.010 -0.147
SMC 3 0.019 0.027 0.018 -0.413
SMC 5 0.017 0.024 0.014 -0.535
SMC 8 0.023 0.022 0.013 0.068
SMC 15 0.022 0.019 0.013 0.221
SMC 30 0.016 0.019 0.012 -0.265
Metro 2 0.127 0.025 0.010 10.304
Metro 3 0.148 0.027 0.018 6.874
Metro 5 0.277 0.024 0.014 17.697
Metro 8 0.308 0.022 0.013 22.483
Metro 15 0.232 0.019 0.013 16.946
Metro 30 0.579 0.019 0.012 47.963
DEMetro_Z 2 0.208 0.025 0.010 18.590
DEMetro_Z 3 0.912 0.027 0.018 50.143
DEMetro_Z 5 3.469 0.024 0.014 241.484
DEMetro_Z 8 5.124 0.022 0.013 401.153
DEMetro_Z 15 5.680 0.019 0.013 451.586
DEMetro_Z 30 6.629 0.019 0.012 566.333
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.360 0.00455 8.505
HMC 3 3.356 0.00455 7.506
HMC 5 3.502 0.00317 4.543
HMC 8 3.510 0.00217 2.080
HMC 15 4.594 0.000275 4.070
HMC 30 4.530 0.000331 4.320
SMC 2 -1.677 0.106 -0.530
SMC 3 -1.173 0.252 -0.366
SMC 5 0.227 0.822 0.086
SMC 8 0.615 0.543 0.222
SMC 15 -1.067 0.297 -0.316
SMC 30 -1.124 0.271 -0.400
Metro 2 4.340 0.000549 5.093
Metro 3 4.505 0.00042 6.313
Metro 5 5.516 6.71e-05 10.780
Metro 8 5.678 4.89e-05 10.287
Metro 15 5.745 4.71e-05 15.327
Metro 30 3.178 0.0067 39.723
DEMetro_Z 2 3.060 0.00728 2.761
DEMetro_Z 3 2.295 0.0377 944.003
DEMetro_Z 5 5.191 0.000137 5050.263
DEMetro_Z 8 9.882 1.08e-07 4672.679
DEMetro_Z 15 18.490 3.11e-11 7239.402
DEMetro_Z 30 24.824 5.65e-13 8634.720
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.596 0.00292 0.929
HMC_vs_SMC 1 3.520 0.0034 0.909
HMC_vs_SMC 2 3.260 0.00569 0.842
HMC_vs_SMC 3 2.944 0.0107 0.760
HMC_vs_SMC 4 5.427 8.92e-05 1.401
HMC_vs_SMC 5 4.719 0.000329 1.219
Metro_vs_DEMetro_Z 0 1.861 0.0839 0.480
Metro_vs_DEMetro_Z 1 -2.280 0.0388 -0.589
Metro_vs_DEMetro_Z 2 -5.177 0.00014 -1.337
Metro_vs_DEMetro_Z 3 -9.846 1.13e-07 -2.542
Metro_vs_DEMetro_Z 4 -18.374 3.38e-11 -4.744
Metro_vs_DEMetro_Z 5 -24.665 6.17e-13 -6.369
HMC_vs_Metro 0 1.442 0.171 0.372
HMC_vs_Metro 1 0.432 0.673 0.111
HMC_vs_Metro 2 -2.467 0.0271 -0.637
HMC_vs_Metro 3 -4.749 0.000311 -1.226
HMC_vs_Metro 4 -3.855 0.00175 -0.995
HMC_vs_Metro 5 -2.745 0.0158 -0.709
HMC_vs_DEMetro_Z 0 2.500 0.0255 0.645
HMC_vs_DEMetro_Z 1 -2.273 0.0393 -0.587
HMC_vs_DEMetro_Z 2 -5.188 0.000138 -1.339
HMC_vs_DEMetro_Z 3 -9.882 1.08e-07 -2.552
HMC_vs_DEMetro_Z 4 -18.498 3.09e-11 -4.776
HMC_vs_DEMetro_Z 5 -24.837 5.61e-13 -6.413
Metro_vs_SMC 0 4.964 0.000208 1.282
Metro_vs_SMC 1 5.052 0.000177 1.304
Metro_vs_SMC 2 5.278 0.000117 1.363
Metro_vs_SMC 3 5.683 5.65e-05 1.467
Metro_vs_SMC 4 5.869 4.08e-05 1.515
Metro_vs_SMC 5 3.248 0.00583 0.839
DEMetro_Z_vs_SMC 0 3.576 0.00304 0.923
DEMetro_Z_vs_SMC 1 2.296 0.0376 0.593
DEMetro_Z_vs_SMC 2 5.192 0.000137 1.341
DEMetro_Z_vs_SMC 3 9.879 1.09e-07 2.551
DEMetro_Z_vs_SMC 4 18.489 3.11e-11 4.774
DEMetro_Z_vs_SMC 5 24.827 5.64e-13 6.410
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.275 0.054 0.026 8.505
HMC 3 0.197 0.038 0.021 7.506
HMC 5 0.133 0.035 0.022 4.543
HMC 8 0.082 0.031 0.025 2.080
HMC 15 0.110 0.030 0.020 4.070
HMC 30 0.124 0.034 0.021 4.320
SMC 2 0.040 0.054 0.026 -0.530
SMC 3 0.031 0.038 0.021 -0.366
SMC 5 0.036 0.035 0.022 0.086
SMC 8 0.036 0.031 0.025 0.222
SMC 15 0.024 0.030 0.020 -0.316
SMC 30 0.026 0.034 0.021 -0.400
Metro 2 0.186 0.054 0.026 5.093
Metro 3 0.172 0.038 0.021 6.313
Metro 5 0.267 0.035 0.022 10.780
Metro 8 0.285 0.031 0.025 10.287
Metro 15 0.334 0.030 0.020 15.327
Metro 30 0.863 0.034 0.021 39.723
DEMetro_Z 2 0.126 0.054 0.026 2.761
DEMetro_Z 3 19.987 0.038 0.021 944.003
DEMetro_Z 5 108.841 0.035 0.022 5050.263
DEMetro_Z 8 115.326 0.031 0.025 4672.679
DEMetro_Z 15 143.536 0.030 0.020 7239.402
DEMetro_Z 30 180.220 0.034 0.021 8634.720
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.120 2.61e-05 36.822
HMC 3 5.943 3.42e-05 19.810
HMC 5 6.310 1.67e-05 13.308
HMC 8 5.175 0.000119 8.251
HMC 15 3.783 0.00192 7.711
HMC 30 5.804 4.2e-05 14.479
SMC 2 -0.805 0.427 -0.314
SMC 3 -1.094 0.286 -0.320
SMC 5 -1.687 0.108 -0.469
SMC 8 0.846 0.405 0.286
SMC 15 0.644 0.525 0.220
SMC 30 -2.255 0.0359 -0.637
Metro 2 7.418 2.39e-06 11.876
Metro 3 6.075 2.43e-05 11.378
Metro 5 6.548 1.23e-05 23.130
Metro 8 8.001 1.27e-06 27.723
Metro 15 10.437 4.45e-08 25.672
Metro 30 7.523 2.76e-06 86.928
DEMetro_Z 2 4.203 0.000874 19.516
DEMetro_Z 3 3.311 0.00515 113.535
DEMetro_Z 5 13.258 2.57e-09 699.730
DEMetro_Z 8 16.560 1.36e-10 866.542
DEMetro_Z 15 35.197 4.57e-15 1170.314
DEMetro_Z 30 49.740 3.74e-17 1645.802
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.624 0.127 -0.419
Metro_vs_DEMetro_Z 1 -2.987 0.0098 -0.771
Metro_vs_DEMetro_Z 2 -13.172 2.8e-09 -3.401
Metro_vs_DEMetro_Z 3 -15.972 2.21e-10 -4.124
Metro_vs_DEMetro_Z 4 -34.290 6.58e-15 -8.854
Metro_vs_DEMetro_Z 5 -45.705 1.22e-16 -11.801
DEMetro_Z_vs_SMC 0 4.269 0.000779 1.102
DEMetro_Z_vs_SMC 1 3.320 0.00506 0.857
DEMetro_Z_vs_SMC 2 13.269 2.55e-09 3.426
DEMetro_Z_vs_SMC 3 16.517 1.41e-10 4.265
DEMetro_Z_vs_SMC 4 35.099 4.76e-15 9.063
DEMetro_Z_vs_SMC 5 49.789 3.7e-17 12.855
HMC_vs_DEMetro_Z 0 2.623 0.02 0.677
HMC_vs_DEMetro_Z 1 -2.651 0.019 -0.685
HMC_vs_DEMetro_Z 2 -13.134 2.91e-09 -3.391
HMC_vs_DEMetro_Z 3 -16.593 1.33e-10 -4.284
HMC_vs_DEMetro_Z 4 -35.507 4.06e-15 -9.168
HMC_vs_DEMetro_Z 5 -47.225 7.72e-17 -12.193
HMC_vs_Metro 0 3.899 0.0016 1.007
HMC_vs_Metro 1 2.047 0.0599 0.529
HMC_vs_Metro 2 -2.186 0.0463 -0.564
HMC_vs_Metro 3 -5.342 0.000104 -1.379
HMC_vs_Metro 4 -4.911 0.000229 -1.268
HMC_vs_Metro 5 -6.032 3.08e-05 -1.558
HMC_vs_SMC 0 6.186 2.37e-05 1.597
HMC_vs_SMC 1 6.071 2.88e-05 1.567
HMC_vs_SMC 2 6.470 1.47e-05 1.671
HMC_vs_SMC 3 4.921 0.000225 1.271
HMC_vs_SMC 4 3.564 0.00311 0.920
HMC_vs_SMC 5 6.042 3.03e-05 1.560
Metro_vs_SMC 0 7.169 4.79e-06 1.851
Metro_vs_SMC 1 6.289 1.99e-05 1.624
Metro_vs_SMC 2 6.778 8.9e-06 1.750
Metro_vs_SMC 3 7.771 1.92e-06 2.007
Metro_vs_SMC 4 10.499 5.09e-08 2.711
Metro_vs_SMC 5 7.590 2.51e-06 1.960
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.343 0.037 0.008 36.822
HMC 3 0.241 0.032 0.011 19.810
HMC 5 0.161 0.030 0.010 13.308
HMC 8 0.103 0.026 0.009 8.251
HMC 15 0.085 0.025 0.008 7.711
HMC 30 0.120 0.026 0.006 14.479
SMC 2 0.034 0.037 0.008 -0.314
SMC 3 0.028 0.032 0.011 -0.320
SMC 5 0.025 0.030 0.010 -0.469
SMC 8 0.028 0.026 0.009 0.286
SMC 15 0.027 0.025 0.008 0.220
SMC 30 0.022 0.026 0.006 -0.637
Metro 2 0.135 0.037 0.008 11.876
Metro 3 0.152 0.032 0.011 11.378
Metro 5 0.258 0.030 0.010 23.130
Metro 8 0.286 0.026 0.009 27.723
Metro 15 0.226 0.025 0.008 25.672
Metro 30 0.585 0.026 0.006 86.928
DEMetro_Z 2 0.199 0.037 0.008 19.516
DEMetro_Z 3 1.233 0.032 0.011 113.535
DEMetro_Z 5 6.941 0.030 0.010 699.730
DEMetro_Z 8 8.162 0.026 0.009 866.542
DEMetro_Z 15 9.213 0.025 0.008 1170.314
DEMetro_Z 30 10.606 0.026 0.006 1645.802
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.322 1.86e-05 40.488
HMC 3 5.785 4.51e-05 19.328
HMC 5 5.559 6.56e-05 14.671
HMC 8 5.093 0.000149 10.736
HMC 15 3.580 0.00292 9.045
HMC 30 7.827 1.3e-06 13.101
SMC 2 -0.878 0.389 -0.408
SMC 3 -1.537 0.138 -0.459
SMC 5 -1.341 0.193 -0.408
SMC 8 1.233 0.228 0.475
SMC 15 0.605 0.55 0.234
SMC 30 -2.536 0.0185 -0.764
Metro 2 6.745 7.04e-06 10.401
Metro 3 6.052 2.29e-05 8.939
Metro 5 7.624 2.07e-06 18.339
Metro 8 10.124 6.6e-08 25.300
Metro 15 10.287 5.47e-08 26.749
Metro 30 8.741 4.72e-07 65.629
DEMetro_Z 2 4.217 0.000851 19.675
DEMetro_Z 3 7.477 2.79e-06 26.018
DEMetro_Z 5 39.521 5.11e-16 97.568
DEMetro_Z 8 45.456 7.06e-17 112.942
DEMetro_Z 15 56.465 2.27e-18 114.280
DEMetro_Z 30 61.965 4.72e-19 114.088
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.286 0.000754 1.107
DEMetro_Z_vs_SMC 1 7.536 2.73e-06 1.946
DEMetro_Z_vs_SMC 2 40.247 7.13e-16 10.392
DEMetro_Z_vs_SMC 3 46.124 1.07e-16 11.909
DEMetro_Z_vs_SMC 4 60.040 2.72e-18 15.502
DEMetro_Z_vs_SMC 5 62.775 1.46e-18 16.209
HMC_vs_Metro 0 4.672 0.00036 1.206
HMC_vs_Metro 1 2.610 0.0206 0.674
HMC_vs_Metro 2 -1.008 0.331 -0.260
HMC_vs_Metro 3 -5.903 3.85e-05 -1.524
HMC_vs_Metro 4 -4.133 0.00102 -1.067
HMC_vs_Metro 5 -6.912 7.19e-06 -1.785
Metro_vs_DEMetro_Z 0 -2.042 0.0605 -0.527
Metro_vs_DEMetro_Z 1 -4.278 0.000766 -1.105
Metro_vs_DEMetro_Z 2 -26.490 2.32e-13 -6.840
Metro_vs_DEMetro_Z 3 -21.802 3.33e-12 -5.629
Metro_vs_DEMetro_Z 4 -28.185 9.86e-14 -7.277
Metro_vs_DEMetro_Z 5 -6.380 1.71e-05 -1.647
HMC_vs_SMC 0 6.342 1.82e-05 1.637
HMC_vs_SMC 1 5.983 3.35e-05 1.545
HMC_vs_SMC 2 5.561 7.02e-05 1.436
HMC_vs_SMC 3 4.698 0.000342 1.213
HMC_vs_SMC 4 3.409 0.00423 0.880
HMC_vs_SMC 5 8.084 1.21e-06 2.087
Metro_vs_SMC 0 6.470 1.47e-05 1.670
Metro_vs_SMC 1 6.391 1.68e-05 1.650
Metro_vs_SMC 2 8.059 1.26e-06 2.081
Metro_vs_SMC 3 9.750 1.28e-07 2.518
Metro_vs_SMC 4 10.320 6.32e-08 2.665
Metro_vs_SMC 5 8.871 4.03e-07 2.290
HMC_vs_DEMetro_Z 0 2.964 0.0103 0.765
HMC_vs_DEMetro_Z 1 -1.231 0.239 -0.318
HMC_vs_DEMetro_Z 2 -28.199 9.79e-14 -7.281
HMC_vs_DEMetro_Z 3 -35.977 3.38e-15 -9.289
HMC_vs_DEMetro_Z 4 -31.644 2e-14 -8.170
HMC_vs_DEMetro_Z 5 -53.430 1.38e-17 -13.796
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.166 0.015 0.004 40.488
HMC 3 0.142 0.015 0.007 19.328
HMC 5 0.112 0.015 0.007 14.671
HMC 8 0.072 0.014 0.005 10.736
HMC 15 0.058 0.014 0.005 9.045
HMC 30 0.080 0.016 0.005 13.101
SMC 2 0.014 0.015 0.004 -0.408
SMC 3 0.012 0.015 0.007 -0.459
SMC 5 0.013 0.015 0.007 -0.408
SMC 8 0.016 0.014 0.005 0.475
SMC 15 0.015 0.014 0.005 0.234
SMC 30 0.012 0.016 0.005 -0.764
Metro 2 0.054 0.015 0.004 10.401
Metro 3 0.074 0.015 0.007 8.939
Metro 5 0.136 0.015 0.007 18.339
Metro 8 0.152 0.014 0.005 25.300
Metro 15 0.146 0.014 0.005 26.749
Metro 30 0.336 0.016 0.005 65.629
DEMetro_Z 2 0.089 0.015 0.004 19.675
DEMetro_Z 3 0.186 0.015 0.007 26.018
DEMetro_Z 5 0.659 0.015 0.007 97.568
DEMetro_Z 8 0.630 0.014 0.005 112.942
DEMetro_Z 15 0.579 0.014 0.005 114.280
DEMetro_Z 30 0.573 0.016 0.005 114.088
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 6.078 2.82e-05 48.497
HMC 3 4.543 0.000448 16.030
HMC 5 6.024 2.93e-05 17.723
HMC 8 8.304 7.19e-07 17.700
HMC 15 6.403 1.32e-05 10.898
HMC 30 8.692 2.92e-07 11.605
SMC 2 0.965 0.344 0.422
SMC 3 -1.783 0.0905 -0.501
SMC 5 -0.996 0.328 -0.325
SMC 8 -0.801 0.43 -0.283
SMC 15 0.664 0.512 0.266
SMC 30 -0.097 0.923 -0.040
Metro 2 4.010 0.00126 13.142
Metro 3 3.384 0.00397 4.027
Metro 5 4.965 0.000199 15.170
Metro 8 3.830 0.00183 25.168
Metro 15 3.693 0.0024 33.373
Metro 30 6.165 2.43e-05 48.765
DEMetro_Z 2 3.680 0.00246 23.382
DEMetro_Z 3 3.366 0.0046 22.138
DEMetro_Z 5 5.224 0.000129 506.615
DEMetro_Z 8 5.454 8.49e-05 503.052
DEMetro_Z 15 21.340 4.45e-12 712.889
DEMetro_Z 30 31.370 2.25e-14 1027.769
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 4.501 0.000498 1.162
HMC_vs_DEMetro_Z 1 -0.773 0.452 -0.200
HMC_vs_DEMetro_Z 2 -5.083 0.000167 -1.313
HMC_vs_DEMetro_Z 3 -5.223 0.000129 -1.349
HMC_vs_DEMetro_Z 4 -20.897 5.93e-12 -5.396
HMC_vs_DEMetro_Z 5 -31.451 2.17e-14 -8.121
Metro_vs_SMC 0 3.636 0.0027 0.939
Metro_vs_SMC 1 4.059 0.00117 1.048
Metro_vs_SMC 2 5.085 0.000166 1.313
Metro_vs_SMC 3 3.825 0.00186 0.988
Metro_vs_SMC 4 3.706 0.00235 0.957
Metro_vs_SMC 5 6.211 2.27e-05 1.604
Metro_vs_DEMetro_Z 0 -1.246 0.233 -0.322
Metro_vs_DEMetro_Z 1 -2.790 0.0145 -0.720
Metro_vs_DEMetro_Z 2 -5.000 0.000194 -1.291
Metro_vs_DEMetro_Z 3 -5.031 0.000184 -1.299
Metro_vs_DEMetro_Z 4 -18.403 3.31e-11 -4.752
Metro_vs_DEMetro_Z 5 -28.496 8.48e-14 -7.358
HMC_vs_Metro 0 3.614 0.00282 0.933
HMC_vs_Metro 1 3.713 0.00232 0.959
HMC_vs_Metro 2 0.601 0.557 0.155
HMC_vs_Metro 3 -1.156 0.267 -0.298
HMC_vs_Metro 4 -2.480 0.0265 -0.640
HMC_vs_Metro 5 -4.562 0.000443 -1.178
HMC_vs_SMC 0 6.129 2.61e-05 1.583
HMC_vs_SMC 1 4.773 0.000297 1.232
HMC_vs_SMC 2 6.110 2.7e-05 1.577
HMC_vs_SMC 3 8.269 9.29e-07 2.135
HMC_vs_SMC 4 6.424 1.59e-05 1.659
HMC_vs_SMC 5 8.594 5.9e-07 2.219
DEMetro_Z_vs_SMC 0 3.666 0.00254 0.947
DEMetro_Z_vs_SMC 1 3.457 0.00385 0.893
DEMetro_Z_vs_SMC 2 5.228 0.000128 1.350
DEMetro_Z_vs_SMC 3 5.455 8.48e-05 1.408
DEMetro_Z_vs_SMC 4 21.263 4.68e-12 5.490
DEMetro_Z_vs_SMC 5 31.179 2.45e-14 8.050
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.503 0.025 0.010 48.497
HMC 3 0.310 0.027 0.018 16.030
HMC 5 0.277 0.024 0.014 17.723
HMC 8 0.247 0.022 0.013 17.700
HMC 15 0.156 0.019 0.013 10.898
HMC 30 0.154 0.019 0.012 11.605
SMC 2 0.030 0.025 0.010 0.422
SMC 3 0.018 0.027 0.018 -0.501
SMC 5 0.020 0.024 0.014 -0.325
SMC 8 0.018 0.022 0.013 -0.283
SMC 15 0.023 0.019 0.013 0.266
SMC 30 0.018 0.019 0.012 -0.040
Metro 2 0.155 0.025 0.010 13.142
Metro 3 0.098 0.027 0.018 4.027
Metro 5 0.241 0.024 0.014 15.170
Metro 8 0.342 0.022 0.013 25.168
Metro 15 0.438 0.019 0.013 33.373
Metro 30 0.588 0.019 0.012 48.765
DEMetro_Z 2 0.256 0.025 0.010 23.382
DEMetro_Z 3 0.417 0.027 0.018 22.138
DEMetro_Z 5 7.251 0.024 0.014 506.615
DEMetro_Z 8 6.420 0.022 0.013 503.052
DEMetro_Z 15 8.955 0.019 0.013 712.889
DEMetro_Z 30 12.014 0.019 0.012 1027.769
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.239 0.000813 18.197
HMC 3 3.354 0.00466 11.051
HMC 5 4.363 0.000611 9.703
HMC 8 6.412 1.07e-05 7.884
HMC 15 4.580 0.000335 5.301
HMC 30 5.368 7.31e-05 6.577
SMC 2 -1.459 0.157 -0.455
SMC 3 -1.261 0.221 -0.364
SMC 5 0.024 0.981 0.008
SMC 8 0.245 0.809 0.072
SMC 15 0.723 0.476 0.244
SMC 30 -0.349 0.73 -0.123
Metro 2 4.099 0.000862 4.342
Metro 3 5.883 3.02e-05 8.245
Metro 5 5.521 6.42e-05 9.603
Metro 8 5.533 6.68e-05 12.240
Metro 15 4.297 0.000719 14.414
Metro 30 7.799 1.65e-06 21.686
DEMetro_Z 2 3.563 0.003 7.991
DEMetro_Z 3 1.504 0.155 240.109
DEMetro_Z 5 2.166 0.048 2877.939
DEMetro_Z 8 5.909 3.81e-05 672.179
DEMetro_Z 15 9.683 1.39e-07 1024.817
DEMetro_Z 30 13.231 2.64e-09 1083.376
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 4.388 0.000619 1.133
HMC_vs_SMC 1 3.414 0.00419 0.882
HMC_vs_SMC 2 4.332 0.00069 1.118
HMC_vs_SMC 3 7.005 6.2e-06 1.809
HMC_vs_SMC 4 4.521 0.00048 1.167
HMC_vs_SMC 5 5.338 0.000105 1.378
Metro_vs_DEMetro_Z 0 -1.335 0.203 -0.345
Metro_vs_DEMetro_Z 1 -1.447 0.17 -0.374
Metro_vs_DEMetro_Z 2 -2.159 0.0487 -0.557
Metro_vs_DEMetro_Z 3 -5.840 4.29e-05 -1.508
Metro_vs_DEMetro_Z 4 -9.524 1.7e-07 -2.459
Metro_vs_DEMetro_Z 5 -12.878 3.76e-09 -3.325
HMC_vs_Metro 0 2.969 0.0102 0.767
HMC_vs_Metro 1 0.800 0.437 0.207
HMC_vs_Metro 2 0.035 0.973 0.009
HMC_vs_Metro 3 -1.844 0.0864 -0.476
HMC_vs_Metro 4 -2.548 0.0232 -0.658
HMC_vs_Metro 5 -4.696 0.000344 -1.213
HMC_vs_DEMetro_Z 0 2.821 0.0136 0.728
HMC_vs_DEMetro_Z 1 -1.429 0.175 -0.369
HMC_vs_DEMetro_Z 2 -2.159 0.0487 -0.558
HMC_vs_DEMetro_Z 3 -5.860 4.14e-05 -1.513
HMC_vs_DEMetro_Z 4 -9.711 1.34e-07 -2.507
HMC_vs_DEMetro_Z 5 -13.237 2.63e-09 -3.418
Metro_vs_SMC 0 4.444 0.000556 1.147
Metro_vs_SMC 1 6.107 2.71e-05 1.577
Metro_vs_SMC 2 5.636 6.14e-05 1.455
Metro_vs_SMC 3 5.617 6.35e-05 1.450
Metro_vs_SMC 4 4.126 0.00103 1.065
Metro_vs_SMC 5 7.648 2.3e-06 1.975
DEMetro_Z_vs_SMC 0 3.774 0.00205 0.974
DEMetro_Z_vs_SMC 1 1.506 0.154 0.389
DEMetro_Z_vs_SMC 2 2.167 0.048 0.559
DEMetro_Z_vs_SMC 3 5.910 3.8e-05 1.526
DEMetro_Z_vs_SMC 4 9.676 1.4e-07 2.498
DEMetro_Z_vs_SMC 5 13.244 2.61e-09 3.420
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.528 0.054 0.026 18.197
HMC 3 0.272 0.038 0.021 11.051
HMC 5 0.244 0.035 0.022 9.703
HMC 8 0.225 0.031 0.025 7.884
HMC 15 0.135 0.030 0.020 5.301
HMC 30 0.171 0.034 0.021 6.577
SMC 2 0.042 0.054 0.026 -0.455
SMC 3 0.031 0.038 0.021 -0.364
SMC 5 0.035 0.035 0.022 0.008
SMC 8 0.033 0.031 0.025 0.072
SMC 15 0.035 0.030 0.020 0.244
SMC 30 0.032 0.034 0.021 -0.123
Metro 2 0.167 0.054 0.026 4.342
Metro 3 0.213 0.038 0.021 8.245
Metro 5 0.242 0.035 0.022 9.603
Metro 8 0.333 0.031 0.025 12.240
Metro 15 0.316 0.030 0.020 14.414
Metro 30 0.487 0.034 0.021 21.686
DEMetro_Z 2 0.262 0.054 0.026 7.991
DEMetro_Z 3 5.112 0.038 0.021 240.109
DEMetro_Z 5 62.039 0.035 0.022 2877.939
DEMetro_Z 8 16.616 0.031 0.025 672.179
DEMetro_Z 15 20.345 0.030 0.020 1024.817
DEMetro_Z 30 22.642 0.034 0.021 1083.376
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.773 4.79e-05 49.747
HMC 3 4.539 0.000457 22.627
HMC 5 6.311 1.81e-05 20.705
HMC 8 8.828 3.44e-07 19.179
HMC 15 6.462 1.32e-05 14.517
HMC 30 8.495 5.44e-07 17.927
SMC 2 0.199 0.844 0.077
SMC 3 -1.138 0.269 -0.320
SMC 5 -0.653 0.519 -0.215
SMC 8 0.086 0.932 0.029
SMC 15 1.276 0.213 0.495
SMC 30 -0.864 0.395 -0.337
Metro 2 4.850 0.000249 16.198
Metro 3 7.635 1.37e-06 9.492
Metro 5 5.766 4.67e-05 19.839
Metro 8 4.689 0.000346 30.647
Metro 15 4.056 0.00118 48.404
Metro 30 6.605 1.17e-05 74.203
DEMetro_Z 2 3.761 0.0021 25.792
DEMetro_Z 3 3.517 0.00341 37.163
DEMetro_Z 5 5.133 0.000152 629.582
DEMetro_Z 8 6.529 1.34e-05 599.167
DEMetro_Z 15 21.272 4.65e-12 988.030
DEMetro_Z 30 28.950 6.81e-14 1559.140
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.072 0.302 -0.277
Metro_vs_DEMetro_Z 1 -2.588 0.0215 -0.668
Metro_vs_DEMetro_Z 2 -4.908 0.000231 -1.267
Metro_vs_DEMetro_Z 3 -6.041 3.03e-05 -1.560
Metro_vs_DEMetro_Z 4 -18.830 2.43e-11 -4.862
Metro_vs_DEMetro_Z 5 -26.922 1.85e-13 -6.951
DEMetro_Z_vs_SMC 0 3.784 0.00201 0.977
DEMetro_Z_vs_SMC 1 3.557 0.00315 0.918
DEMetro_Z_vs_SMC 2 5.136 0.000151 1.326
DEMetro_Z_vs_SMC 3 6.524 1.35e-05 1.684
DEMetro_Z_vs_SMC 4 21.221 4.81e-12 5.479
DEMetro_Z_vs_SMC 5 28.869 7.09e-14 7.454
HMC_vs_DEMetro_Z 0 3.727 0.00225 0.962
HMC_vs_DEMetro_Z 1 -1.148 0.27 -0.296
HMC_vs_DEMetro_Z 2 -4.994 0.000197 -1.289
HMC_vs_DEMetro_Z 3 -6.273 2.05e-05 -1.620
HMC_vs_DEMetro_Z 4 -20.896 5.93e-12 -5.395
HMC_vs_DEMetro_Z 5 -28.900 6.98e-14 -7.462
HMC_vs_Metro 0 3.169 0.00683 0.818
HMC_vs_Metro 1 2.908 0.0115 0.751
HMC_vs_Metro 2 0.177 0.862 0.046
HMC_vs_Metro 3 -1.811 0.0916 -0.468
HMC_vs_Metro 4 -2.824 0.0135 -0.729
HMC_vs_Metro 5 -4.914 0.000228 -1.269
HMC_vs_SMC 0 5.847 4.24e-05 1.510
HMC_vs_SMC 1 4.650 0.000375 1.201
HMC_vs_SMC 2 6.317 1.9e-05 1.631
HMC_vs_SMC 3 8.938 3.68e-07 2.308
HMC_vs_SMC 4 6.360 1.77e-05 1.642
HMC_vs_SMC 5 8.525 6.48e-07 2.201
Metro_vs_SMC 0 4.681 0.000354 1.209
Metro_vs_SMC 1 8.143 1.11e-06 2.103
Metro_vs_SMC 2 5.772 4.83e-05 1.490
Metro_vs_SMC 3 4.666 0.000364 1.205
Metro_vs_SMC 4 4.035 0.00123 1.042
Metro_vs_SMC 5 6.655 1.09e-05 1.718
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.450 0.037 0.008 49.747
HMC 3 0.271 0.032 0.011 22.627
HMC 5 0.234 0.030 0.010 20.705
HMC 8 0.206 0.026 0.009 19.179
HMC 15 0.139 0.025 0.008 14.517
HMC 30 0.142 0.026 0.006 17.927
SMC 2 0.037 0.037 0.008 0.077
SMC 3 0.028 0.032 0.011 -0.320
SMC 5 0.028 0.030 0.010 -0.215
SMC 8 0.026 0.026 0.009 0.029
SMC 15 0.029 0.025 0.008 0.495
SMC 30 0.024 0.026 0.006 -0.337
Metro 2 0.171 0.037 0.008 16.198
Metro 3 0.132 0.032 0.011 9.492
Metro 5 0.226 0.030 0.010 19.839
Metro 8 0.313 0.026 0.009 30.647
Metro 15 0.405 0.025 0.008 48.404
Metro 30 0.503 0.026 0.006 74.203
DEMetro_Z 2 0.251 0.037 0.008 25.792
DEMetro_Z 3 0.425 0.032 0.011 37.163
DEMetro_Z 5 6.248 0.030 0.010 629.582
DEMetro_Z 8 5.652 0.026 0.009 599.167
DEMetro_Z 15 7.782 0.025 0.008 988.030
DEMetro_Z 30 10.049 0.026 0.006 1559.140
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.735 5.13e-05 56.053
HMC 3 4.597 0.000409 22.471
HMC 5 6.081 2.72e-05 22.693
HMC 8 8.129 1.05e-06 27.687
HMC 15 6.323 1.75e-05 18.268
HMC 30 8.579 4.87e-07 18.547
SMC 2 -1.122 0.272 -0.460
SMC 3 -1.625 0.121 -0.457
SMC 5 -0.990 0.331 -0.312
SMC 8 -0.024 0.981 -0.008
SMC 15 1.470 0.153 0.586
SMC 30 -1.481 0.15 -0.537
Metro 2 5.008 0.00018 12.710
Metro 3 7.079 3.21e-06 8.316
Metro 5 6.244 1.97e-05 16.659
Metro 8 5.805 4.49e-05 32.625
Metro 15 5.276 0.000116 41.471
Metro 30 7.727 2.02e-06 63.546
DEMetro_Z 2 3.743 0.00218 27.346
DEMetro_Z 3 4.770 0.000292 18.423
DEMetro_Z 5 14.952 5.13e-10 108.586
DEMetro_Z 8 18.449 3.11e-11 155.638
DEMetro_Z 15 55.646 5.37e-18 184.830
DEMetro_Z 30 58.296 2.78e-18 192.778
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.827 0.00185 0.988
DEMetro_Z_vs_SMC 1 4.963 0.000208 1.281
DEMetro_Z_vs_SMC 2 14.933 5.4e-10 3.856
DEMetro_Z_vs_SMC 3 18.350 3.44e-11 4.738
DEMetro_Z_vs_SMC 4 54.483 1.05e-17 14.068
DEMetro_Z_vs_SMC 5 57.460 5.02e-18 14.836
HMC_vs_Metro 0 3.890 0.00163 1.004
HMC_vs_Metro 1 3.088 0.00803 0.797
HMC_vs_Metro 2 1.401 0.183 0.362
HMC_vs_Metro 3 -0.829 0.421 -0.214
HMC_vs_Metro 4 -2.875 0.0122 -0.742
HMC_vs_Metro 5 -5.405 9.28e-05 -1.395
Metro_vs_DEMetro_Z 0 -1.644 0.122 -0.424
Metro_vs_DEMetro_Z 1 -2.383 0.0319 -0.615
Metro_vs_DEMetro_Z 2 -10.830 3.45e-08 -2.796
Metro_vs_DEMetro_Z 3 -10.605 4.49e-08 -2.738
Metro_vs_DEMetro_Z 4 -15.999 2.16e-10 -4.131
Metro_vs_DEMetro_Z 5 -14.306 9.51e-10 -3.694
HMC_vs_SMC 0 5.860 4.14e-05 1.513
HMC_vs_SMC 1 4.730 0.000323 1.221
HMC_vs_SMC 2 6.132 2.6e-05 1.583
HMC_vs_SMC 3 8.221 9.95e-07 2.123
HMC_vs_SMC 4 6.193 2.34e-05 1.599
HMC_vs_SMC 5 8.972 3.52e-07 2.316
Metro_vs_SMC 0 5.069 0.000171 1.309
Metro_vs_SMC 1 7.805 1.82e-06 2.015
Metro_vs_SMC 2 6.320 1.89e-05 1.632
Metro_vs_SMC 3 5.804 4.57e-05 1.498
Metro_vs_SMC 4 5.236 0.000126 1.352
Metro_vs_SMC 5 7.743 2e-06 1.999
HMC_vs_DEMetro_Z 0 4.078 0.00113 1.053
HMC_vs_DEMetro_Z 1 0.774 0.452 0.200
HMC_vs_DEMetro_Z 2 -11.545 1.53e-08 -2.981
HMC_vs_DEMetro_Z 3 -12.280 6.95e-09 -3.171
HMC_vs_DEMetro_Z 4 -34.734 5.5e-15 -8.968
HMC_vs_DEMetro_Z 5 -53.113 1.5e-17 -13.714
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.224 0.015 0.004 56.053
HMC 3 0.163 0.015 0.007 22.471
HMC 5 0.165 0.015 0.007 22.693
HMC 8 0.165 0.014 0.005 27.687
HMC 15 0.104 0.014 0.005 18.268
HMC 30 0.106 0.016 0.005 18.547
SMC 2 0.013 0.015 0.004 -0.460
SMC 3 0.012 0.015 0.007 -0.457
SMC 5 0.013 0.015 0.007 -0.312
SMC 8 0.014 0.014 0.005 -0.008
SMC 15 0.016 0.014 0.005 0.586
SMC 30 0.013 0.016 0.005 -0.537
Metro 2 0.063 0.015 0.004 12.710
Metro 3 0.070 0.015 0.007 8.316
Metro 5 0.125 0.015 0.007 16.659
Metro 8 0.192 0.014 0.005 32.625
Metro 15 0.219 0.014 0.005 41.471
Metro 30 0.326 0.016 0.005 63.546
DEMetro_Z 2 0.117 0.015 0.004 27.346
DEMetro_Z 3 0.136 0.015 0.007 18.423
DEMetro_Z 5 0.732 0.015 0.007 108.586
DEMetro_Z 8 0.864 0.014 0.005 155.638
DEMetro_Z 15 0.929 0.014 0.005 184.830
DEMetro_Z 30 0.957 0.016 0.005 192.778
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

Vary_Dimension_with_Tails_and_MM (Mixture, dimension, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.580 0.00251 3.594
HMC 3 2.579 0.0196 2.189
HMC 5 2.688 0.0143 1.652
HMC 8 1.314 0.209 1.858
HMC 15 0.322 0.75 0.096
HMC 30 3.964 0.00105 3.556
SMC 2 3.753 0.00169 3.535
SMC 3 4.975 0.000183 9.568
SMC 5 6.284 1.71e-05 12.127
SMC 8 16.550 1.34e-10 147.541
SMC 15 19.521 3.12e-16 9.268
SMC 30 29.077 3.96e-14 72.642
Metro 2 5.058 3.5e-05 2.374
Metro 3 2.300 0.0346 1.979
Metro 5 2.720 0.0133 1.683
Metro 8 6.137 4.52e-06 3.493
Metro 15 1.485 0.152 0.435
Metro 30 4.780 0.000284 15.778
DEMetro_Z 2 5.053 0.000144 7.163
DEMetro_Z 3 5.630 6.16e-05 45.395
DEMetro_Z 5 6.618 1.13e-05 36.336
DEMetro_Z 8 5.044 0.000179 376.341
DEMetro_Z 15 8.623 5.36e-07 36.765
DEMetro_Z 30 23.142 1.46e-12 340.727
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.952 0.0712 -0.504
HMC_vs_DEMetro_Z 1 -5.354 0.000102 -1.382
HMC_vs_DEMetro_Z 2 -6.298 1.96e-05 -1.626
HMC_vs_DEMetro_Z 3 -5.003 0.000193 -1.292
HMC_vs_DEMetro_Z 4 -8.638 5.54e-07 -2.230
HMC_vs_DEMetro_Z 5 -22.452 2.23e-12 -5.797
Metro_vs_SMC 0 -1.429 0.175 -0.369
Metro_vs_SMC 1 -3.585 0.00299 -0.926
Metro_vs_SMC 2 -5.781 4.76e-05 -1.493
Metro_vs_SMC 3 -16.045 2.08e-10 -4.143
Metro_vs_SMC 4 -21.356 4.41e-12 -5.514
Metro_vs_SMC 5 -16.481 1.46e-10 -4.255
Metro_vs_DEMetro_Z 0 -3.518 0.00341 -0.908
Metro_vs_DEMetro_Z 1 -5.616 6.36e-05 -1.450
Metro_vs_DEMetro_Z 2 -6.505 1.39e-05 -1.680
Metro_vs_DEMetro_Z 3 -4.999 0.000195 -1.291
Metro_vs_DEMetro_Z 4 -8.537 6.37e-07 -2.204
Metro_vs_DEMetro_Z 5 -22.219 2.57e-12 -5.737
HMC_vs_Metro 0 1.085 0.296 0.280
HMC_vs_Metro 1 0.194 0.849 0.050
HMC_vs_Metro 2 -0.065 0.949 -0.017
HMC_vs_Metro 3 -0.962 0.353 -0.248
HMC_vs_Metro 4 -1.719 0.108 -0.444
HMC_vs_Metro 5 -3.588 0.00297 -0.926
HMC_vs_SMC 0 0.041 0.968 0.010
HMC_vs_SMC 1 -4.881 0.000243 -1.260
HMC_vs_SMC 2 -5.114 0.000158 -1.320
HMC_vs_SMC 3 -16.307 1.68e-10 -4.210
HMC_vs_SMC 4 -20.586 7.27e-12 -5.315
HMC_vs_SMC 5 -24.604 6.38e-13 -6.353
DEMetro_Z_vs_SMC 0 2.650 0.019 0.684
DEMetro_Z_vs_SMC 1 4.184 0.000918 1.080
DEMetro_Z_vs_SMC 2 4.930 0.000222 1.273
DEMetro_Z_vs_SMC 3 2.961 0.0103 0.765
DEMetro_Z_vs_SMC 4 6.360 1.77e-05 1.642
DEMetro_Z_vs_SMC 5 17.986 4.51e-11 4.644
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.184 0.047 0.038 3.594
HMC 3 0.136 0.085 0.023 2.189
HMC 5 0.164 0.082 0.050 1.652
HMC 8 0.203 0.091 0.060 1.858
HMC 15 0.100 0.091 0.095 0.096
HMC 30 0.127 0.067 0.017 3.556
SMC 2 0.182 0.047 0.038 3.535
SMC 3 0.309 0.085 0.023 9.568
SMC 5 0.684 0.082 0.050 12.127
SMC 8 8.961 0.091 0.060 147.541
SMC 15 0.968 0.091 0.095 9.268
SMC 30 1.292 0.067 0.017 72.642
Metro 2 0.138 0.047 0.038 2.374
Metro 3 0.131 0.085 0.023 1.979
Metro 5 0.166 0.082 0.050 1.683
Metro 8 0.301 0.091 0.060 3.493
Metro 15 0.132 0.091 0.095 0.435
Metro 30 0.333 0.067 0.017 15.778
DEMetro_Z 2 0.321 0.047 0.038 7.163
DEMetro_Z 3 1.146 0.085 0.023 45.395
DEMetro_Z 5 1.885 0.082 0.050 36.336
DEMetro_Z 8 22.716 0.091 0.060 376.341
DEMetro_Z 15 3.570 0.091 0.095 36.765
DEMetro_Z 30 5.815 0.067 0.017 340.727
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.346 0.199 -0.350
HMC 3 -0.349 0.731 -0.101
HMC 5 0.858 0.405 1.508
HMC 8 -1.123 0.28 -0.292
HMC 15 -1.031 0.32 -0.266
HMC 30 0.791 0.437 0.381
SMC 2 -1.292 0.217 -0.335
SMC 3 9.017 1.21e-08 5.107
SMC 5 8.669 1.96e-07 8.729
SMC 8 56.653 5.78e-18 485.563
SMC 15 21.655 6.93e-14 5.899
SMC 30 140.808 4.65e-26 143.586
Metro 2 -1.397 0.184 -0.363
Metro 3 -0.140 0.89 -0.040
Metro 5 0.828 0.421 1.460
Metro 8 -1.018 0.324 -0.272
Metro 15 -1.052 0.31 -0.272
Metro 30 1.753 0.1 2.715
DEMetro_Z 2 -1.343 0.2 -0.349
DEMetro_Z 3 2.286 0.038 5.717
DEMetro_Z 5 2.778 0.0143 4.806
DEMetro_Z 8 3.813 0.0019 332.272
DEMetro_Z 15 3.006 0.00562 1.024
DEMetro_Z 30 16.514 9.61e-11 37.563
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.491 0.631 -0.127
HMC_vs_SMC 1 -9.272 2.36e-07 -2.394
HMC_vs_SMC 2 -6.441 1.54e-05 -1.663
HMC_vs_SMC 3 -56.666 6.1e-18 -14.631
HMC_vs_SMC 4 -70.378 2.96e-19 -18.172
HMC_vs_SMC 5 -153.932 5.24e-24 -39.745
Metro_vs_DEMetro_Z 0 -1.755 0.101 -0.453
Metro_vs_DEMetro_Z 1 -2.291 0.038 -0.591
Metro_vs_DEMetro_Z 2 -3.249 0.00583 -0.839
Metro_vs_DEMetro_Z 3 -3.815 0.00189 -0.985
Metro_vs_DEMetro_Z 4 -5.792 4.67e-05 -1.495
Metro_vs_DEMetro_Z 5 -16.086 2.01e-10 -4.153
HMC_vs_Metro 0 0.621 0.545 0.160
HMC_vs_Metro 1 -2.350 0.034 -0.607
HMC_vs_Metro 2 0.812 0.43 0.210
HMC_vs_Metro 3 -0.282 0.782 -0.073
HMC_vs_Metro 4 1.887 0.0801 0.487
HMC_vs_Metro 5 -1.498 0.156 -0.387
HMC_vs_DEMetro_Z 0 -0.052 0.96 -0.013
HMC_vs_DEMetro_Z 1 -2.315 0.0363 -0.598
HMC_vs_DEMetro_Z 2 -3.202 0.0064 -0.827
HMC_vs_DEMetro_Z 3 -3.816 0.00189 -0.985
HMC_vs_DEMetro_Z 4 -5.795 4.65e-05 -1.496
HMC_vs_DEMetro_Z 5 -16.205 1.82e-10 -4.184
Metro_vs_SMC 0 -0.862 0.403 -0.223
Metro_vs_SMC 1 -9.370 2.08e-07 -2.419
Metro_vs_SMC 2 -6.428 1.58e-05 -1.660
Metro_vs_SMC 3 -56.570 6.24e-18 -14.606
Metro_vs_SMC 4 -70.789 2.73e-19 -18.278
Metro_vs_SMC 5 -79.369 5.53e-20 -20.493
DEMetro_Z_vs_SMC 0 -0.424 0.678 -0.109
DEMetro_Z_vs_SMC 1 0.245 0.81 0.063
DEMetro_Z_vs_SMC 2 -2.655 0.0189 -0.685
DEMetro_Z_vs_SMC 3 -1.668 0.117 -0.431
DEMetro_Z_vs_SMC 4 -22.592 2.05e-12 -5.833
DEMetro_Z_vs_SMC 5 -52.093 1.97e-17 -13.450
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.146 21.314 46.211 -0.350
HMC 3 6.276 8.077 17.919 -0.101
HMC 5 89.000 17.798 47.221 1.508
HMC 8 9.449 30.578 72.429 -0.292
HMC 15 6.866 73.927 251.794 -0.266
HMC 30 14.428 8.923 14.446 0.381
SMC 2 5.848 21.314 46.211 -0.335
SMC 3 99.598 8.077 17.919 5.107
SMC 5 430.011 17.798 47.221 8.729
SMC 8 35199.268 30.578 72.429 485.563
SMC 15 1559.342 73.927 251.794 5.899
SMC 30 2083.163 8.923 14.446 143.586
Metro 2 4.562 21.314 46.211 -0.363
Metro 3 7.361 8.077 17.919 -0.040
Metro 5 86.729 17.798 47.221 1.460
Metro 8 10.843 30.578 72.429 -0.272
Metro 15 5.484 73.927 251.794 -0.272
Metro 30 48.141 8.923 14.446 2.715
DEMetro_Z 2 5.201 21.314 46.211 -0.349
DEMetro_Z 3 110.519 8.077 17.919 5.717
DEMetro_Z 5 244.745 17.798 47.221 4.806
DEMetro_Z 8 24096.629 30.578 72.429 332.272
DEMetro_Z 15 331.785 73.927 251.794 1.024
DEMetro_Z 30 551.563 8.923 14.446 37.563
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.923 0.00778 1.510
HMC 3 3.683 0.00187 3.104
HMC 5 2.758 0.013 2.011
HMC 8 2.145 0.0488 3.072
HMC 15 3.581 0.00145 1.625
HMC 30 2.044 0.0602 12.309
SMC 2 8.533 1.55e-08 4.334
SMC 3 13.830 1.46e-09 142.633
SMC 5 20.654 6.82e-12 234.820
SMC 8 97.651 3.03e-21 2540.948
SMC 15 129.266 2.91e-23 364.126
SMC 30 264.588 2.02e-27 1333.647
Metro 2 4.253 0.000315 1.268
Metro 3 6.239 5.93e-06 4.224
Metro 5 3.470 0.00276 2.544
Metro 8 3.627 0.00267 9.505
Metro 15 4.094 0.000336 1.617
Metro 30 4.558 0.000446 61.703
DEMetro_Z 2 5.245 5.39e-05 3.758
DEMetro_Z 3 4.252 0.000805 87.859
DEMetro_Z 5 6.041 3.02e-05 82.020
DEMetro_Z 8 8.430 7.41e-07 1450.558
DEMetro_Z 15 13.149 2.82e-09 130.516
DEMetro_Z 30 32.408 1.42e-14 628.296
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.615 0.00281 -0.933
Metro_vs_DEMetro_Z 1 -4.048 0.0012 -1.045
Metro_vs_DEMetro_Z 2 -5.850 4.22e-05 -1.511
Metro_vs_DEMetro_Z 3 -8.369 8.07e-07 -2.161
Metro_vs_DEMetro_Z 4 -12.929 3.57e-09 -3.338
Metro_vs_DEMetro_Z 5 -22.259 2.51e-12 -5.747
DEMetro_Z_vs_SMC 0 -0.814 0.429 -0.210
DEMetro_Z_vs_SMC 1 -2.431 0.0291 -0.628
DEMetro_Z_vs_SMC 2 -7.398 3.36e-06 -1.910
DEMetro_Z_vs_SMC 3 -5.890 3.94e-05 -1.521
DEMetro_Z_vs_SMC 4 -24.557 6.55e-13 -6.341
DEMetro_Z_vs_SMC 5 -39.008 1.1e-15 -10.072
HMC_vs_DEMetro_Z 0 -2.535 0.0238 -0.655
HMC_vs_DEMetro_Z 1 -4.095 0.00109 -1.057
HMC_vs_DEMetro_Z 2 -5.815 4.48e-05 -1.501
HMC_vs_DEMetro_Z 3 -8.417 7.54e-07 -2.173
HMC_vs_DEMetro_Z 4 -13.104 3e-09 -3.384
HMC_vs_DEMetro_Z 5 -31.550 2.08e-14 -8.146
HMC_vs_Metro 0 0.455 0.656 0.118
HMC_vs_Metro 1 -1.359 0.196 -0.351
HMC_vs_Metro 2 -1.099 0.29 -0.284
HMC_vs_Metro 3 -2.064 0.058 -0.533
HMC_vs_Metro 4 0.017 0.987 0.004
HMC_vs_Metro 5 -3.566 0.0031 -0.921
HMC_vs_SMC 0 -4.648 0.000376 -1.200
HMC_vs_SMC 1 -13.855 1.45e-09 -3.577
HMC_vs_SMC 2 -21.058 5.34e-12 -5.437
HMC_vs_SMC 3 -95.314 4.28e-21 -24.610
HMC_vs_SMC 4 -126.384 8.28e-23 -32.632
HMC_vs_SMC 5 -199.119 1.43e-25 -51.412
Metro_vs_SMC 0 -7.456 3.08e-06 -1.925
Metro_vs_SMC 1 -13.586 1.87e-09 -3.508
Metro_vs_SMC 2 -20.714 6.68e-12 -5.348
Metro_vs_SMC 3 -93.388 5.69e-21 -24.113
Metro_vs_SMC 4 -135.436 3.14e-23 -34.969
Metro_vs_SMC 5 -84.498 2.3e-20 -21.817
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.255 0.145 0.072 1.510
HMC 3 0.220 0.137 0.027 3.104
HMC 5 0.239 0.138 0.050 2.011
HMC 8 0.315 0.146 0.055 3.072
HMC 15 0.277 0.146 0.081 1.625
HMC 30 0.441 0.121 0.026 12.309
SMC 2 0.459 0.145 0.072 4.334
SMC 3 3.932 0.137 0.027 142.633
SMC 5 11.939 0.138 0.050 234.820
SMC 8 139.333 0.146 0.055 2540.948
SMC 15 29.514 0.146 0.081 364.126
SMC 30 34.791 0.121 0.026 1333.647
Metro 2 0.237 0.145 0.072 1.268
Metro 3 0.250 0.137 0.027 4.224
Metro 5 0.266 0.138 0.050 2.544
Metro 8 0.667 0.146 0.055 9.505
Metro 15 0.276 0.146 0.081 1.617
Metro 30 1.725 0.121 0.026 61.703
DEMetro_Z 2 0.417 0.145 0.072 3.758
DEMetro_Z 3 2.475 0.137 0.027 87.859
DEMetro_Z 5 4.260 0.138 0.050 82.020
DEMetro_Z 8 79.604 0.146 0.055 1450.558
DEMetro_Z 15 10.673 0.146 0.081 130.516
DEMetro_Z 30 16.454 0.121 0.026 628.296
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.128 0.00698 4.694
HMC 3 3.861 0.00126 3.211
HMC 5 4.670 0.000284 5.563
HMC 8 2.246 0.0413 12.511
HMC 15 5.532 6.37e-05 9.997
HMC 30 3.807 0.00192 35.946
SMC 2 7.500 1.06e-06 6.773
SMC 3 25.577 2.68e-13 73.742
SMC 5 73.973 3.37e-20 133.058
SMC 8 94.300 6.12e-22 149.555
SMC 15 121.951 2.27e-24 145.756
SMC 30 179.775 9.09e-26 333.048
Metro 2 4.711 0.000107 2.504
Metro 3 5.061 6.24e-05 3.118
Metro 5 8.793 4.91e-08 6.012
Metro 8 8.296 8.18e-07 26.859
Metro 15 10.144 2.75e-08 11.036
Metro 30 6.716 9.83e-06 146.771
DEMetro_Z 2 4.753 0.00028 9.023
DEMetro_Z 3 7.897 1.53e-06 38.687
DEMetro_Z 5 12.689 4.35e-09 74.803
DEMetro_Z 8 43.205 2.06e-16 164.141
DEMetro_Z 15 53.228 9.1e-18 157.279
DEMetro_Z 30 57.591 4.44e-18 393.863
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.270 0.225 0.328
DEMetro_Z_vs_SMC 1 -6.607 1.18e-05 -1.706
DEMetro_Z_vs_SMC 2 -9.331 2.19e-07 -2.409
DEMetro_Z_vs_SMC 3 3.819 0.00188 0.986
DEMetro_Z_vs_SMC 4 3.618 0.0028 0.934
DEMetro_Z_vs_SMC 5 7.748 1.98e-06 2.000
HMC_vs_Metro 0 1.275 0.223 0.329
HMC_vs_Metro 1 0.097 0.924 0.025
HMC_vs_Metro 2 -0.338 0.741 -0.087
HMC_vs_Metro 3 -1.922 0.0752 -0.496
HMC_vs_Metro 4 -0.588 0.566 -0.152
HMC_vs_Metro 5 -4.794 0.000286 -1.238
Metro_vs_DEMetro_Z 0 -3.475 0.00372 -0.897
Metro_vs_DEMetro_Z 1 -7.236 4.32e-06 -1.868
Metro_vs_DEMetro_Z 2 -12.212 7.46e-09 -3.153
Metro_vs_DEMetro_Z 3 -30.912 2.76e-14 -7.982
Metro_vs_DEMetro_Z 4 -42.068 3.86e-16 -10.862
Metro_vs_DEMetro_Z 5 -10.760 3.74e-08 -2.778
HMC_vs_SMC 0 -1.109 0.286 -0.286
HMC_vs_SMC 1 -28.235 9.62e-14 -7.290
HMC_vs_SMC 2 -57.132 5.44e-18 -14.752
HMC_vs_SMC 3 -24.298 7.57e-13 -6.274
HMC_vs_SMC 4 -67.255 5.59e-19 -17.365
HMC_vs_SMC 5 -31.288 2.33e-14 -8.079
Metro_vs_SMC 0 -4.173 0.000938 -1.078
Metro_vs_SMC 1 -25.142 4.74e-13 -6.492
Metro_vs_SMC 2 -63.633 1.21e-18 -16.430
Metro_vs_SMC 3 -30.857 2.83e-14 -7.967
Metro_vs_SMC 4 -78.304 6.68e-20 -20.218
Metro_vs_SMC 5 -8.409 7.63e-07 -2.171
HMC_vs_DEMetro_Z 0 -1.607 0.13 -0.415
HMC_vs_DEMetro_Z 1 -7.020 6.06e-06 -1.813
HMC_vs_DEMetro_Z 2 -11.074 2.6e-08 -2.859
HMC_vs_DEMetro_Z 3 -26.615 2.17e-13 -6.872
HMC_vs_DEMetro_Z 4 -44.152 1.97e-16 -11.400
HMC_vs_DEMetro_Z 5 -31.230 2.4e-14 -8.063
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.034 0.010 0.005 4.694
HMC 3 0.027 0.014 0.004 3.211
HMC 5 0.032 0.013 0.004 5.563
HMC 8 0.052 0.013 0.003 12.511
HMC 15 0.044 0.015 0.003 9.997
HMC 30 0.057 0.014 0.001 35.946
SMC 2 0.045 0.010 0.005 6.773
SMC 3 0.315 0.014 0.004 73.742
SMC 5 0.483 0.013 0.004 133.058
SMC 8 0.481 0.013 0.003 149.555
SMC 15 0.432 0.015 0.003 145.756
SMC 30 0.409 0.014 0.001 333.048
Metro 2 0.023 0.010 0.005 2.504
Metro 3 0.026 0.014 0.004 3.118
Metro 5 0.034 0.013 0.004 6.012
Metro 8 0.097 0.013 0.003 26.859
Metro 15 0.047 0.015 0.003 11.036
Metro 30 0.188 0.014 0.001 146.771
DEMetro_Z 2 0.056 0.010 0.005 9.023
DEMetro_Z 3 0.172 0.014 0.004 38.687
DEMetro_Z 5 0.277 0.013 0.004 74.803
DEMetro_Z 8 0.527 0.013 0.003 164.141
DEMetro_Z 15 0.465 0.015 0.003 157.279
DEMetro_Z 30 0.481 0.014 0.001 393.863
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.503 0.000365 4.562
HMC 3 2.752 0.0148 3.779
HMC 5 2.429 0.0253 1.608
HMC 8 0.499 0.622 0.187
HMC 15 0.762 0.452 0.308
HMC 30 1.646 0.122 10.035
SMC 2 4.219 0.000609 3.755
SMC 3 5.351 0.000101 30.102
SMC 5 4.308 0.000688 10.492
SMC 8 11.490 1.6e-08 95.308
SMC 15 11.550 1.83e-09 9.569
SMC 30 30.993 1.47e-14 71.028
Metro 2 1.082 0.298 24.000
Metro 3 1.870 0.0821 4.412
Metro 5 3.938 0.00091 2.663
Metro 8 4.231 0.000399 2.497
Metro 15 2.244 0.0346 0.681
Metro 30 6.466 7.36e-06 6.185
DEMetro_Z 2 5.438 6.07e-05 6.160
DEMetro_Z 3 3.156 0.00699 19.331
DEMetro_Z 5 3.214 0.00623 45.079
DEMetro_Z 8 4.667 0.000363 215.855
DEMetro_Z 15 8.333 7.89e-07 29.822
DEMetro_Z 30 13.809 1.51e-09 374.944
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.135 0.276 -0.293
HMC_vs_DEMetro_Z 1 -2.675 0.0181 -0.691
HMC_vs_DEMetro_Z 2 -3.123 0.00748 -0.806
HMC_vs_DEMetro_Z 3 -4.666 0.000364 -1.205
HMC_vs_DEMetro_Z 4 -8.723 4.93e-07 -2.252
HMC_vs_DEMetro_Z 5 -14.187 1.06e-09 -3.663
Metro_vs_SMC 0 0.932 0.367 0.241
Metro_vs_SMC 1 -4.097 0.00109 -1.058
Metro_vs_SMC 2 -2.911 0.0114 -0.751
Metro_vs_SMC 3 -11.242 2.15e-08 -2.903
Metro_vs_SMC 4 -10.552 4.78e-08 -2.725
Metro_vs_SMC 5 -23.738 1.04e-12 -6.129
Metro_vs_DEMetro_Z 0 0.800 0.437 0.207
Metro_vs_DEMetro_Z 1 -2.318 0.0361 -0.598
Metro_vs_DEMetro_Z 2 -3.040 0.00882 -0.785
Metro_vs_DEMetro_Z 3 -4.602 0.000411 -1.188
Metro_vs_DEMetro_Z 4 -8.095 1.19e-06 -2.090
Metro_vs_DEMetro_Z 5 -13.666 1.73e-09 -3.529
HMC_vs_Metro 0 -0.875 0.396 -0.226
HMC_vs_Metro 1 -0.214 0.834 -0.055
HMC_vs_Metro 2 -2.138 0.0506 -0.552
HMC_vs_Metro 3 -3.766 0.00208 -0.972
HMC_vs_Metro 4 -1.258 0.229 -0.325
HMC_vs_Metro 5 0.613 0.55 0.158
HMC_vs_SMC 0 0.540 0.597 0.140
HMC_vs_SMC 1 -4.200 0.000891 -1.084
HMC_vs_SMC 2 -3.640 0.00268 -0.940
HMC_vs_SMC 3 -11.517 1.58e-08 -2.974
HMC_vs_SMC 4 -10.432 5.52e-08 -2.694
HMC_vs_SMC 5 -8.785 4.53e-07 -2.268
DEMetro_Z_vs_SMC 0 1.661 0.119 0.429
DEMetro_Z_vs_SMC 1 -1.205 0.248 -0.311
DEMetro_Z_vs_SMC 2 2.446 0.0283 0.632
DEMetro_Z_vs_SMC 3 2.654 0.0189 0.685
DEMetro_Z_vs_SMC 4 5.470 8.26e-05 1.412
DEMetro_Z_vs_SMC 5 11.092 2.55e-08 2.864
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.221 0.047 0.038 4.562
HMC 3 0.173 0.085 0.023 3.779
HMC 5 0.162 0.082 0.050 1.608
HMC 8 0.102 0.091 0.060 0.187
HMC 15 0.120 0.091 0.095 0.308
HMC 30 0.236 0.067 0.017 10.035
SMC 2 0.191 0.047 0.038 3.755
SMC 3 0.789 0.085 0.023 30.102
SMC 5 0.603 0.082 0.050 10.492
SMC 8 5.821 0.091 0.060 95.308
SMC 15 0.996 0.091 0.095 9.569
SMC 30 1.265 0.067 0.017 71.028
Metro 2 0.965 0.047 0.038 24.000
Metro 3 0.188 0.085 0.023 4.412
Metro 5 0.214 0.082 0.050 2.663
Metro 8 0.241 0.091 0.060 2.497
Metro 15 0.155 0.091 0.095 0.681
Metro 30 0.171 0.067 0.017 6.185
DEMetro_Z 2 0.283 0.047 0.038 6.160
DEMetro_Z 3 0.537 0.085 0.023 19.331
DEMetro_Z 5 2.319 0.082 0.050 45.079
DEMetro_Z 8 13.068 0.091 0.060 215.855
DEMetro_Z 15 2.913 0.091 0.095 29.822
DEMetro_Z 30 6.392 0.067 0.017 374.944
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.715 0.484 0.642
HMC 3 0.137 0.892 0.040
HMC 5 0.823 0.423 1.448
HMC 8 -1.322 0.207 -0.342
HMC 15 -0.947 0.359 -0.246
HMC 30 0.552 0.586 0.232
SMC 2 -1.382 0.188 -0.358
SMC 3 3.682 0.00133 1.983
SMC 5 5.874 2.65e-05 6.644
SMC 8 20.709 6.66e-12 383.981
SMC 15 18.108 1.27e-14 5.340
SMC 30 105.617 4.32e-23 139.760
Metro 2 0.880 0.394 2.838
Metro 3 0.509 0.615 0.183
Metro 5 0.837 0.416 1.475
Metro 8 -1.134 0.276 -0.294
Metro 15 -1.052 0.311 -0.272
Metro 30 -0.346 0.732 -0.103
DEMetro_Z 2 -1.345 0.2 -0.349
DEMetro_Z 3 1.400 0.183 3.657
DEMetro_Z 5 2.386 0.0315 7.063
DEMetro_Z 8 2.411 0.0302 133.704
DEMetro_Z 15 0.949 0.353 0.277
DEMetro_Z 30 6.715 9.25e-06 21.797
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.159 0.266 0.299
HMC_vs_SMC 1 -3.816 0.00189 -0.985
HMC_vs_SMC 2 -5.630 6.21e-05 -1.454
HMC_vs_SMC 3 -20.730 6.61e-12 -5.352
HMC_vs_SMC 4 -38.028 1.57e-15 -9.819
HMC_vs_SMC 5 -89.474 1.04e-20 -23.102
Metro_vs_DEMetro_Z 0 0.990 0.339 0.256
Metro_vs_DEMetro_Z 1 -1.320 0.208 -0.341
Metro_vs_DEMetro_Z 2 -2.083 0.0561 -0.538
Metro_vs_DEMetro_Z 3 -2.416 0.0299 -0.624
Metro_vs_DEMetro_Z 4 -4.032 0.00124 -1.041
Metro_vs_DEMetro_Z 5 -6.869 7.7e-06 -1.774
HMC_vs_Metro 0 -0.647 0.528 -0.167
HMC_vs_Metro 1 -0.653 0.525 -0.169
HMC_vs_Metro 2 -1.752 0.102 -0.452
HMC_vs_Metro 3 -1.978 0.068 -0.511
HMC_vs_Metro 4 1.095 0.292 0.283
HMC_vs_Metro 5 0.999 0.335 0.258
HMC_vs_DEMetro_Z 0 1.148 0.27 0.296
HMC_vs_DEMetro_Z 1 -1.386 0.188 -0.358
HMC_vs_DEMetro_Z 2 -2.095 0.0548 -0.541
HMC_vs_DEMetro_Z 3 -2.417 0.0299 -0.624
HMC_vs_DEMetro_Z 4 -4.216 0.000862 -1.089
HMC_vs_DEMetro_Z 5 -6.598 1.19e-05 -1.704
Metro_vs_SMC 0 0.993 0.338 0.256
Metro_vs_SMC 1 -3.517 0.00342 -0.908
Metro_vs_SMC 2 -5.573 6.87e-05 -1.439
Metro_vs_SMC 3 -20.721 6.65e-12 -5.350
Metro_vs_SMC 4 -39.211 1.02e-15 -10.124
Metro_vs_SMC 5 -105.596 1.02e-21 -27.265
DEMetro_Z_vs_SMC 0 0.726 0.48 0.187
DEMetro_Z_vs_SMC 1 0.693 0.5 0.179
DEMetro_Z_vs_SMC 2 0.146 0.886 0.038
DEMetro_Z_vs_SMC 3 -4.617 0.000399 -1.192
DEMetro_Z_vs_SMC 4 -28.170 9.94e-14 -7.273
DEMetro_Z_vs_SMC 5 -32.905 1.16e-14 -8.496
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 50.977 21.314 46.211 0.642
HMC 3 8.791 8.077 17.919 0.040
HMC 5 86.158 17.798 47.221 1.448
HMC 8 5.800 30.578 72.429 -0.342
HMC 15 12.034 73.927 251.794 -0.246
HMC 30 12.273 8.923 14.446 0.232
SMC 2 4.749 21.314 46.211 -0.358
SMC 3 43.619 8.077 17.919 1.983
SMC 5 331.523 17.798 47.221 6.644
SMC 8 27841.809 30.578 72.429 383.981
SMC 15 1418.453 73.927 251.794 5.340
SMC 30 2027.886 8.923 14.446 139.760
Metro 2 152.451 21.314 46.211 2.838
Metro 3 11.348 8.077 17.919 0.183
Metro 5 87.445 17.798 47.221 1.475
Metro 8 9.262 30.578 72.429 -0.294
Metro 15 5.527 73.927 251.794 -0.272
Metro 30 7.430 8.923 14.446 -0.103
DEMetro_Z 2 5.187 21.314 46.211 -0.349
DEMetro_Z 3 73.601 8.077 17.919 3.657
DEMetro_Z 5 351.299 17.798 47.221 7.063
DEMetro_Z 8 9714.609 30.578 72.429 133.704
DEMetro_Z 15 143.699 73.927 251.794 0.277
DEMetro_Z 30 323.801 8.923 14.446 21.797
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.782 0.0135 2.936
HMC 3 4.968 0.000139 4.941
HMC 5 2.786 0.0122 2.003
HMC 8 1.989 0.0567 0.761
HMC 15 1.454 0.167 2.685
HMC 30 1.651 0.121 21.440
SMC 2 4.891 5.08e-05 2.240
SMC 3 8.080 1.21e-06 82.800
SMC 5 17.565 6.1e-11 196.259
SMC 8 38.063 1.55e-15 2244.089
SMC 15 69.543 2.9e-19 344.872
SMC 30 199.509 1.2e-25 1315.244
Metro 2 1.102 0.289 11.883
Metro 3 2.898 0.0114 6.377
Metro 5 4.600 0.000225 3.358
Metro 8 5.616 3.28e-05 4.852
Metro 15 4.644 0.000149 2.715
Metro 30 3.973 0.00137 16.773
DEMetro_Z 2 5.437 2.43e-05 3.216
DEMetro_Z 3 2.359 0.0334 44.365
DEMetro_Z 5 3.254 0.00577 78.159
DEMetro_Z 8 4.527 0.000474 859.608
DEMetro_Z 15 7.674 2.2e-06 82.018
DEMetro_Z 30 12.245 7.2e-09 471.945
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.800 0.437 0.207
Metro_vs_DEMetro_Z 1 -2.018 0.0631 -0.521
Metro_vs_DEMetro_Z 2 -3.114 0.00761 -0.804
Metro_vs_DEMetro_Z 3 -4.495 0.000504 -1.161
Metro_vs_DEMetro_Z 4 -7.408 3.31e-06 -1.913
Metro_vs_DEMetro_Z 5 -11.947 9.9e-09 -3.085
DEMetro_Z_vs_SMC 0 1.912 0.0765 0.494
DEMetro_Z_vs_SMC 1 -2.295 0.0377 -0.592
DEMetro_Z_vs_SMC 2 -3.980 0.00137 -1.028
DEMetro_Z_vs_SMC 3 -7.491 2.92e-06 -1.934
DEMetro_Z_vs_SMC 4 -23.585 1.14e-12 -6.090
DEMetro_Z_vs_SMC 5 -21.184 4.92e-12 -5.470
HMC_vs_DEMetro_Z 0 -0.243 0.812 -0.063
HMC_vs_DEMetro_Z 1 -2.118 0.0525 -0.547
HMC_vs_DEMetro_Z 2 -3.170 0.00681 -0.819
HMC_vs_DEMetro_Z 3 -4.523 0.000477 -1.168
HMC_vs_DEMetro_Z 4 -7.844 1.72e-06 -2.025
HMC_vs_DEMetro_Z 5 -10.907 3.16e-08 -2.816
HMC_vs_Metro 0 -0.831 0.42 -0.215
HMC_vs_Metro 1 -0.628 0.54 -0.162
HMC_vs_Metro 2 -3.035 0.00891 -0.784
HMC_vs_Metro 3 -4.496 0.000503 -1.161
HMC_vs_Metro 4 -0.017 0.987 -0.004
HMC_vs_Metro 5 0.339 0.74 0.088
HMC_vs_SMC 0 0.604 0.555 0.156
HMC_vs_SMC 1 -7.468 3.02e-06 -1.928
HMC_vs_SMC 2 -17.671 5.72e-11 -4.563
HMC_vs_SMC 3 -38.117 1.52e-15 -9.842
HMC_vs_SMC 4 -63.647 1.21e-18 -16.433
HMC_vs_SMC 5 -69.731 3.37e-19 -18.004
Metro_vs_SMC 0 0.908 0.379 0.234
Metro_vs_SMC 1 -7.553 2.66e-06 -1.950
Metro_vs_SMC 2 -17.426 6.9e-11 -4.499
Metro_vs_SMC 3 -37.979 1.6e-15 -9.806
Metro_vs_SMC 4 -67.314 5.52e-19 -17.380
Metro_vs_SMC 5 -151.213 6.73e-24 -39.043
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.358 0.145 0.072 2.936
HMC 3 0.269 0.137 0.027 4.941
HMC 5 0.238 0.138 0.050 2.003
HMC 8 0.188 0.146 0.055 0.761
HMC 15 0.362 0.146 0.081 2.685
HMC 30 0.678 0.121 0.026 21.440
SMC 2 0.307 0.145 0.072 2.240
SMC 3 2.340 0.137 0.027 82.800
SMC 5 10.001 0.138 0.050 196.259
SMC 8 123.072 0.146 0.055 2244.089
SMC 15 27.961 0.146 0.081 344.872
SMC 30 34.312 0.121 0.026 1315.244
Metro 2 1.005 0.145 0.072 11.883
Metro 3 0.307 0.137 0.027 6.377
Metro 5 0.307 0.138 0.050 3.358
Metro 8 0.412 0.146 0.055 4.852
Metro 15 0.365 0.146 0.081 2.715
Metro 30 0.557 0.121 0.026 16.773
DEMetro_Z 2 0.378 0.145 0.072 3.216
DEMetro_Z 3 1.318 0.137 0.027 44.365
DEMetro_Z 5 4.066 0.138 0.050 78.159
DEMetro_Z 8 47.233 0.146 0.055 859.608
DEMetro_Z 15 6.761 0.146 0.081 82.018
DEMetro_Z 30 12.390 0.121 0.026 471.945
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.326 6.93e-05 5.409
HMC 3 3.928 0.00136 5.805
HMC 5 4.636 0.000325 6.557
HMC 8 3.546 0.0029 4.643
HMC 15 2.247 0.0412 13.127
HMC 30 2.520 0.0245 64.169
SMC 2 4.805 0.000209 5.375
SMC 3 13.240 2.42e-09 59.891
SMC 5 73.467 3.24e-20 126.412
SMC 8 84.408 4.71e-21 149.599
SMC 15 136.991 1.38e-25 147.713
SMC 30 124.526 4.65e-23 336.459
Metro 2 2.818 0.0125 3.034
Metro 3 4.133 0.000714 3.542
Metro 5 5.657 4.04e-05 6.494
Metro 8 6.432 1.4e-05 15.330
Metro 15 7.227 3.77e-06 16.382
Metro 30 5.524 7.47e-05 71.172
DEMetro_Z 2 4.577 0.000369 6.669
DEMetro_Z 3 3.396 0.00433 19.857
DEMetro_Z 5 6.167 2.44e-05 71.611
DEMetro_Z 8 49.140 3.22e-17 172.515
DEMetro_Z 15 25.968 2.83e-13 161.032
DEMetro_Z 30 43.448 2.37e-16 427.661
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 0.739 0.472 0.191
DEMetro_Z_vs_SMC 1 -6.131 2.6e-05 -1.583
DEMetro_Z_vs_SMC 2 -4.838 0.000263 -1.249
DEMetro_Z_vs_SMC 3 6.346 1.81e-05 1.638
DEMetro_Z_vs_SMC 4 2.150 0.0495 0.555
DEMetro_Z_vs_SMC 5 8.567 6.11e-07 2.212
HMC_vs_Metro 0 1.778 0.0972 0.459
HMC_vs_Metro 1 1.478 0.161 0.382
HMC_vs_Metro 2 0.050 0.961 0.013
HMC_vs_Metro 3 -3.983 0.00136 -1.029
HMC_vs_Metro 4 -0.634 0.536 -0.164
HMC_vs_Metro 5 -0.245 0.81 -0.063
Metro_vs_DEMetro_Z 0 -1.849 0.0857 -0.477
Metro_vs_DEMetro_Z 1 -2.943 0.0107 -0.760
Metro_vs_DEMetro_Z 2 -5.830 4.37e-05 -1.505
Metro_vs_DEMetro_Z 3 -39.685 8.67e-16 -10.247
Metro_vs_DEMetro_Z 4 -23.048 1.56e-12 -5.951
Metro_vs_DEMetro_Z 5 -25.114 4.81e-13 -6.485
HMC_vs_SMC 0 0.021 0.984 0.005
HMC_vs_SMC 1 -10.222 7.11e-08 -2.639
HMC_vs_SMC 2 -58.940 3.52e-18 -15.218
HMC_vs_SMC 3 -59.003 3.47e-18 -15.235
HMC_vs_SMC 4 -23.183 1.44e-12 -5.986
HMC_vs_SMC 5 -10.565 4.71e-08 -2.728
Metro_vs_SMC 0 -2.311 0.0366 -0.597
Metro_vs_SMC 1 -11.644 1.38e-08 -3.006
Metro_vs_SMC 2 -54.450 1.06e-17 -14.059
Metro_vs_SMC 3 -49.879 3.61e-17 -12.879
Metro_vs_SMC 4 -55.603 7.94e-18 -14.357
Metro_vs_SMC 5 -20.315 8.7e-12 -5.245
HMC_vs_DEMetro_Z 0 -0.750 0.466 -0.194
HMC_vs_DEMetro_Z 1 -2.411 0.0302 -0.622
HMC_vs_DEMetro_Z 2 -5.863 4.13e-05 -1.514
HMC_vs_DEMetro_Z 3 -39.924 7.98e-16 -10.308
HMC_vs_DEMetro_Z 4 -20.691 6.78e-12 -5.342
HMC_vs_DEMetro_Z 5 -14.546 7.64e-10 -3.756
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.038 0.010 0.005 5.409
HMC 3 0.037 0.014 0.004 5.805
HMC 5 0.036 0.013 0.004 6.557
HMC 8 0.028 0.013 0.003 4.643
HMC 15 0.053 0.015 0.003 13.127
HMC 30 0.090 0.014 0.001 64.169
SMC 2 0.037 0.010 0.005 5.375
SMC 3 0.258 0.014 0.004 59.891
SMC 5 0.460 0.013 0.004 126.412
SMC 8 0.481 0.013 0.003 149.599
SMC 15 0.438 0.015 0.003 147.713
SMC 30 0.413 0.014 0.001 336.459
Metro 2 0.025 0.010 0.005 3.034
Metro 3 0.028 0.014 0.004 3.542
Metro 5 0.036 0.013 0.004 6.494
Metro 8 0.061 0.013 0.003 15.330
Metro 15 0.062 0.015 0.003 16.382
Metro 30 0.099 0.014 0.001 71.172
DEMetro_Z 2 0.044 0.010 0.005 6.669
DEMetro_Z 3 0.095 0.014 0.004 19.857
DEMetro_Z 5 0.266 0.013 0.004 71.611
DEMetro_Z 8 0.553 0.013 0.003 172.515
DEMetro_Z 15 0.476 0.015 0.003 161.032
DEMetro_Z 30 0.521 0.014 0.001 427.661
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
3
5
8
15
30
Chain
2
3
5
8
15
30

three_attr_mm

▼

Varying_Mode_Distance_with_Dim_and_Corr (Mixture, mm, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.452 0.000517 10.547
HMC 4 5.345 8.81e-05 9.008
HMC 6 5.220 0.000108 8.011
HMC 8 5.638 4.55e-05 7.334
HMC 10 7.348 2.99e-06 14.751
HMC 12 4.978 0.00018 9.134
SMC 0 1.486 0.15 0.667
SMC 4 -0.300 0.767 -0.115
SMC 6 0.780 0.443 0.358
SMC 8 -0.617 0.543 -0.196
SMC 10 0.649 0.523 0.321
SMC 12 0.365 0.718 0.116
Metro 0 4.971 0.000205 62.275
Metro 4 5.285 0.000114 33.432
Metro 6 5.555 7.05e-05 55.734
Metro 8 4.349 0.000664 37.867
Metro 10 4.122 0.00103 25.256
Metro 12 4.388 0.000616 35.601
DEMetro_Z 0 27.713 1.24e-13 660.741
DEMetro_Z 4 29.406 5.46e-14 638.320
DEMetro_Z 6 38.496 1.31e-15 655.302
DEMetro_Z 8 26.578 2.2e-13 593.101
DEMetro_Z 10 23.213 1.41e-12 660.481
DEMetro_Z 12 25.881 3.16e-13 460.556
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -26.963 1.82e-13 -6.962
HMC_vs_DEMetro_Z 1 -28.895 7e-14 -7.461
HMC_vs_DEMetro_Z 2 -38.542 1.3e-15 -9.951
HMC_vs_DEMetro_Z 3 -26.192 2.7e-13 -6.763
HMC_vs_DEMetro_Z 4 -22.598 2.04e-12 -5.835
HMC_vs_DEMetro_Z 5 -26.464 2.35e-13 -6.833
Metro_vs_SMC 0 4.896 0.000236 1.264
Metro_vs_SMC 1 5.336 0.000105 1.378
Metro_vs_SMC 2 5.570 6.91e-05 1.438
Metro_vs_SMC 3 4.404 0.0006 1.137
Metro_vs_SMC 4 4.069 0.00115 1.051
Metro_vs_SMC 5 4.375 0.000635 1.130
Metro_vs_DEMetro_Z 0 -19.820 1.22e-11 -5.118
Metro_vs_DEMetro_Z 1 -25.922 3.12e-13 -6.693
Metro_vs_DEMetro_Z 2 -31.036 2.61e-14 -8.013
Metro_vs_DEMetro_Z 3 -21.007 5.52e-12 -5.424
Metro_vs_DEMetro_Z 4 -23.460 1.22e-12 -6.057
Metro_vs_DEMetro_Z 5 -23.630 1.11e-12 -6.101
HMC_vs_Metro 0 -4.175 0.000935 -1.078
HMC_vs_Metro 1 -3.660 0.00257 -0.945
HMC_vs_Metro 2 -4.634 0.000387 -1.196
HMC_vs_Metro 3 -3.353 0.00473 -0.866
HMC_vs_Metro 4 -1.473 0.163 -0.380
HMC_vs_Metro 5 -3.109 0.0077 -0.803
HMC_vs_SMC 0 3.863 0.00172 0.997
HMC_vs_SMC 1 5.753 5e-05 1.485
HMC_vs_SMC 2 4.858 0.000253 1.254
HMC_vs_SMC 3 6.166 2.45e-05 1.592
HMC_vs_SMC 4 7.294 3.95e-06 1.883
HMC_vs_SMC 5 4.835 0.000264 1.249
DEMetro_Z_vs_SMC 0 27.649 1.28e-13 7.139
DEMetro_Z_vs_SMC 1 29.365 5.6e-14 7.582
DEMetro_Z_vs_SMC 2 38.098 1.53e-15 9.837
DEMetro_Z_vs_SMC 3 26.567 2.22e-13 6.860
DEMetro_Z_vs_SMC 4 23.267 1.37e-12 6.007
DEMetro_Z_vs_SMC 5 25.772 3.38e-13 6.654
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.113 0.016 0.009 10.547
HMC 4 0.109 0.016 0.010 9.008
HMC 6 0.097 0.019 0.010 8.011
HMC 8 0.101 0.020 0.011 7.334
HMC 10 0.168 0.017 0.010 14.751
HMC 12 0.145 0.023 0.013 9.134
SMC 0 0.022 0.016 0.009 0.667
SMC 4 0.015 0.016 0.010 -0.115
SMC 6 0.023 0.019 0.010 0.358
SMC 8 0.017 0.020 0.011 -0.196
SMC 10 0.021 0.017 0.010 0.321
SMC 12 0.024 0.023 0.013 0.116
Metro 0 0.591 0.016 0.009 62.275
Metro 4 0.362 0.016 0.010 33.432
Metro 6 0.563 0.019 0.010 55.734
Metro 8 0.438 0.020 0.011 37.867
Metro 10 0.275 0.017 0.010 25.256
Metro 12 0.498 0.023 0.013 35.601
DEMetro_Z 0 6.116 0.016 0.009 660.741
DEMetro_Z 4 6.633 0.016 0.010 638.320
DEMetro_Z 6 6.417 0.019 0.010 655.302
DEMetro_Z 8 6.567 0.020 0.011 593.101
DEMetro_Z 10 6.746 0.017 0.010 660.481
DEMetro_Z 12 6.176 0.023 0.013 460.556
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 3.167 0.00645 4.806
HMC 4 4.060 0.00102 5.616
HMC 6 5.146 9.55e-05 5.010
HMC 8 5.643 5.56e-05 13.550
HMC 10 5.984 2.86e-05 11.341
HMC 12 4.271 0.000718 8.195
SMC 0 0.484 0.632 0.206
SMC 4 0.742 0.464 0.262
SMC 6 -1.982 0.0595 -0.601
SMC 8 4.089 0.000583 2.505
SMC 10 0.083 0.935 0.032
SMC 12 -0.253 0.802 -0.094
Metro 0 2.988 0.00977 47.060
Metro 4 5.112 0.000157 33.325
Metro 6 4.363 0.000644 27.069
Metro 8 2.787 0.0146 158.347
Metro 10 5.076 0.000168 43.077
Metro 12 3.244 0.00587 39.409
DEMetro_Z 0 24.248 7.79e-13 9870.953
DEMetro_Z 4 27.489 1.39e-13 11218.041
DEMetro_Z 6 28.787 7.37e-14 8252.915
DEMetro_Z 8 29.590 5.05e-14 27049.092
DEMetro_Z 10 25.020 5.07e-13 12645.064
DEMetro_Z 12 31.220 2.41e-14 11513.345
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.997 0.00962 0.774
HMC_vs_SMC 1 3.876 0.00168 1.001
HMC_vs_SMC 2 5.882 3.99e-05 1.519
HMC_vs_SMC 3 5.089 0.000165 1.314
HMC_vs_SMC 4 6.158 2.48e-05 1.590
HMC_vs_SMC 5 4.184 0.000919 1.080
Metro_vs_DEMetro_Z 0 -24.057 8.68e-13 -6.211
Metro_vs_DEMetro_Z 1 -27.355 1.49e-13 -7.063
Metro_vs_DEMetro_Z 2 -28.717 7.62e-14 -7.415
Metro_vs_DEMetro_Z 3 -29.146 6.21e-14 -7.525
Metro_vs_DEMetro_Z 4 -24.906 5.4e-13 -6.431
Metro_vs_DEMetro_Z 5 -31.032 2.62e-14 -8.012
HMC_vs_Metro 0 -2.748 0.0157 -0.709
HMC_vs_Metro 1 -4.126 0.00103 -1.065
HMC_vs_Metro 2 -3.424 0.00411 -0.884
HMC_vs_Metro 3 -2.543 0.0234 -0.657
HMC_vs_Metro 4 -3.360 0.00467 -0.868
HMC_vs_Metro 5 -2.573 0.0221 -0.664
HMC_vs_DEMetro_Z 0 -24.247 7.8e-13 -6.260
HMC_vs_DEMetro_Z 1 -27.465 1.41e-13 -7.091
HMC_vs_DEMetro_Z 2 -28.760 7.47e-14 -7.426
HMC_vs_DEMetro_Z 3 -29.537 5.17e-14 -7.627
HMC_vs_DEMetro_Z 4 -24.968 5.22e-13 -6.447
HMC_vs_DEMetro_Z 5 -31.248 2.38e-14 -8.068
Metro_vs_SMC 0 2.996 0.00963 0.774
Metro_vs_SMC 1 4.990 0.000198 1.289
Metro_vs_SMC 2 4.473 0.000525 1.155
Metro_vs_SMC 3 2.750 0.0156 0.710
Metro_vs_SMC 4 5.053 0.000176 1.305
Metro_vs_SMC 5 3.262 0.00568 0.842
DEMetro_Z_vs_SMC 0 24.252 7.77e-13 6.262
DEMetro_Z_vs_SMC 1 27.492 1.39e-13 7.098
DEMetro_Z_vs_SMC 2 28.788 7.37e-14 7.433
DEMetro_Z_vs_SMC 3 29.581 5.07e-14 7.638
DEMetro_Z_vs_SMC 4 25.018 5.07e-13 6.460
DEMetro_Z_vs_SMC 5 31.214 2.41e-14 8.060
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.111 0.029 0.017 4.806
HMC 4 0.105 0.024 0.014 5.616
HMC 6 0.137 0.036 0.020 5.010
HMC 8 0.099 0.019 0.006 13.550
HMC 10 0.172 0.031 0.012 11.341
HMC 12 0.143 0.028 0.014 8.195
SMC 0 0.032 0.029 0.017 0.206
SMC 4 0.028 0.024 0.014 0.262
SMC 6 0.024 0.036 0.020 -0.601
SMC 8 0.034 0.019 0.006 2.505
SMC 10 0.031 0.031 0.012 0.032
SMC 12 0.027 0.028 0.014 -0.094
Metro 0 0.832 0.029 0.017 47.060
Metro 4 0.505 0.024 0.014 33.325
Metro 6 0.578 0.036 0.020 27.069
Metro 8 0.955 0.019 0.006 158.347
Metro 10 0.569 0.031 0.012 43.077
Metro 12 0.581 0.028 0.014 39.409
DEMetro_Z 0 168.420 0.029 0.017 9870.953
DEMetro_Z 4 161.894 0.024 0.014 11218.041
DEMetro_Z 6 165.284 0.036 0.020 8252.915
DEMetro_Z 8 159.768 0.019 0.006 27049.092
DEMetro_Z 10 158.043 0.031 0.012 12645.064
DEMetro_Z 12 161.644 0.028 0.014 11513.345
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 5.350 9.76e-05 16.523
HMC 4 6.648 9.17e-06 12.784
HMC 6 8.332 5.69e-07 12.804
HMC 8 9.813 6.36e-08 13.566
HMC 10 7.930 1.37e-06 23.641
HMC 12 6.397 1.49e-05 15.355
SMC 0 1.821 0.0817 0.908
SMC 4 0.293 0.772 0.105
SMC 6 0.008 0.994 0.004
SMC 8 0.262 0.796 0.083
SMC 10 0.767 0.452 0.416
SMC 12 -0.293 0.772 -0.093
Metro 0 7.064 5.63e-06 106.027
Metro 4 9.053 3.07e-07 56.820
Metro 6 7.501 2.85e-06 83.941
Metro 8 5.759 4.93e-05 81.522
Metro 10 6.854 7.8e-06 55.503
Metro 12 5.840 4.28e-05 64.651
DEMetro_Z 0 66.296 6.79e-19 1874.443
DEMetro_Z 4 58.100 4.28e-18 1642.056
DEMetro_Z 6 66.025 7.18e-19 1720.803
DEMetro_Z 8 66.154 6.99e-19 1749.759
DEMetro_Z 10 59.288 3.23e-18 1904.418
DEMetro_Z 12 74.013 1.45e-19 1369.567
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -50.154 3.34e-17 -12.950
Metro_vs_DEMetro_Z 1 -54.751 9.85e-18 -14.137
Metro_vs_DEMetro_Z 2 -57.450 5.03e-18 -14.833
Metro_vs_DEMetro_Z 3 -54.845 9.61e-18 -14.161
Metro_vs_DEMetro_Z 4 -55.127 8.95e-18 -14.234
Metro_vs_DEMetro_Z 5 -66.356 6.74e-19 -17.133
DEMetro_Z_vs_SMC 0 66.415 6.66e-19 17.148
DEMetro_Z_vs_SMC 1 58.169 4.23e-18 15.019
DEMetro_Z_vs_SMC 2 65.654 7.82e-19 16.952
DEMetro_Z_vs_SMC 3 66.132 7.07e-19 17.075
DEMetro_Z_vs_SMC 4 58.997 3.47e-18 15.233
DEMetro_Z_vs_SMC 5 73.812 1.52e-19 19.058
HMC_vs_DEMetro_Z 0 -65.887 7.44e-19 -17.012
HMC_vs_DEMetro_Z 1 -56.717 6.02e-18 -14.644
HMC_vs_DEMetro_Z 2 -65.887 7.44e-19 -17.012
HMC_vs_DEMetro_Z 3 -66.831 6.1e-19 -17.256
HMC_vs_DEMetro_Z 4 -58.958 3.51e-18 -15.223
HMC_vs_DEMetro_Z 5 -73.564 1.6e-19 -18.994
HMC_vs_Metro 0 -5.712 5.37e-05 -1.475
HMC_vs_Metro 1 -6.779 8.9e-06 -1.750
HMC_vs_Metro 2 -6.011 3.19e-05 -1.552
HMC_vs_Metro 3 -4.698 0.000342 -1.213
HMC_vs_Metro 4 -3.157 0.00699 -0.815
HMC_vs_Metro 5 -4.231 0.000839 -1.092
HMC_vs_SMC 0 4.764 0.000302 1.230
HMC_vs_SMC 1 6.867 7.73e-06 1.773
HMC_vs_SMC 2 8.301 8.89e-07 2.143
HMC_vs_SMC 3 10.347 6.11e-08 2.672
HMC_vs_SMC 4 7.884 1.62e-06 2.036
HMC_vs_SMC 5 6.345 1.81e-05 1.638
Metro_vs_SMC 0 7.056 5.72e-06 1.822
Metro_vs_SMC 1 9.071 3.08e-07 2.342
Metro_vs_SMC 2 7.485 2.94e-06 1.933
Metro_vs_SMC 3 5.775 4.81e-05 1.491
Metro_vs_SMC 4 6.769 9.04e-06 1.748
Metro_vs_SMC 5 5.852 4.21e-05 1.511
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.111 0.022 0.005 16.523
HMC 4 0.102 0.022 0.006 12.784
HMC 6 0.102 0.026 0.006 12.804
HMC 8 0.101 0.023 0.006 13.566
HMC 10 0.150 0.024 0.005 23.641
HMC 12 0.137 0.027 0.007 15.355
SMC 0 0.027 0.022 0.005 0.908
SMC 4 0.023 0.022 0.006 0.105
SMC 6 0.026 0.026 0.006 0.004
SMC 8 0.024 0.023 0.006 0.083
SMC 10 0.026 0.024 0.005 0.416
SMC 12 0.026 0.027 0.007 -0.093
Metro 0 0.593 0.022 0.005 106.027
Metro 4 0.376 0.022 0.006 56.820
Metro 6 0.526 0.026 0.006 83.941
Metro 8 0.492 0.023 0.006 81.522
Metro 10 0.319 0.024 0.005 55.503
Metro 12 0.491 0.027 0.007 64.651
DEMetro_Z 0 10.107 0.022 0.005 1874.443
DEMetro_Z 4 10.263 0.022 0.006 1642.056
DEMetro_Z 6 10.274 0.026 0.006 1720.803
DEMetro_Z 8 10.095 0.023 0.006 1749.759
DEMetro_Z 10 10.150 0.024 0.005 1904.418
DEMetro_Z 12 9.870 0.027 0.007 1369.567
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 5.111 0.000146 11.611
HMC 4 8.972 8.9e-08 7.881
HMC 6 8.115 7.51e-07 11.770
HMC 8 9.874 7.88e-08 18.783
HMC 10 8.682 4.25e-07 19.167
HMC 12 7.863 1.41e-06 17.931
SMC 0 1.155 0.259 0.535
SMC 4 0.008 0.994 0.003
SMC 6 0.592 0.559 0.257
SMC 8 1.208 0.237 0.464
SMC 10 0.567 0.576 0.226
SMC 12 -0.064 0.949 -0.023
Metro 0 7.971 1.41e-06 65.605
Metro 4 8.903 3.72e-07 46.776
Metro 6 7.613 2.4e-06 69.249
Metro 8 7.724 2.04e-06 86.562
Metro 10 8.367 7.79e-07 41.617
Metro 12 6.728 9.57e-06 62.035
DEMetro_Z 0 66.597 1.41e-19 116.055
DEMetro_Z 4 50.139 1.28e-17 102.637
DEMetro_Z 6 113.022 4.03e-24 126.345
DEMetro_Z 8 65.809 4.27e-19 185.041
DEMetro_Z 10 48.915 2.41e-17 118.723
DEMetro_Z 12 62.911 4.59e-19 125.108
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 59.552 3.05e-18 15.376
DEMetro_Z_vs_SMC 1 51.817 2.12e-17 13.379
DEMetro_Z_vs_SMC 2 107.251 8.22e-22 27.692
DEMetro_Z_vs_SMC 3 64.912 9.16e-19 16.760
DEMetro_Z_vs_SMC 4 52.354 1.84e-17 13.518
DEMetro_Z_vs_SMC 5 62.384 1.6e-18 16.107
HMC_vs_Metro 0 -6.124 2.63e-05 -1.581
HMC_vs_Metro 1 -7.474 3e-06 -1.930
HMC_vs_Metro 2 -5.735 5.16e-05 -1.481
HMC_vs_Metro 3 -5.476 8.16e-05 -1.414
HMC_vs_Metro 4 -3.357 0.00469 -0.867
HMC_vs_Metro 5 -4.602 0.000411 -1.188
Metro_vs_DEMetro_Z 0 -5.913 3.78e-05 -1.527
Metro_vs_DEMetro_Z 1 -8.751 4.75e-07 -2.260
Metro_vs_DEMetro_Z 2 -6.546 1.3e-05 -1.690
Metro_vs_DEMetro_Z 3 -8.464 7.06e-07 -2.185
Metro_vs_DEMetro_Z 4 -14.289 9.66e-10 -3.689
Metro_vs_DEMetro_Z 5 -7.675 2.21e-06 -1.982
HMC_vs_SMC 0 4.529 0.000472 1.169
HMC_vs_SMC 1 10.086 8.4e-08 2.604
HMC_vs_SMC 2 7.769 1.92e-06 2.006
HMC_vs_SMC 3 9.847 1.13e-07 2.542
HMC_vs_SMC 4 8.655 5.41e-07 2.235
HMC_vs_SMC 5 7.815 1.8e-06 2.018
Metro_vs_SMC 0 8.025 1.32e-06 2.072
Metro_vs_SMC 1 8.857 4.11e-07 2.287
Metro_vs_SMC 2 7.545 2.69e-06 1.948
Metro_vs_SMC 3 7.678 2.2e-06 1.983
Metro_vs_SMC 4 8.269 9.3e-07 2.135
Metro_vs_SMC 5 6.721 9.77e-06 1.735
HMC_vs_DEMetro_Z 0 -38.585 1.28e-15 -9.963
HMC_vs_DEMetro_Z 1 -41.843 4.16e-16 -10.804
HMC_vs_DEMetro_Z 2 -59.983 2.76e-18 -15.488
HMC_vs_DEMetro_Z 3 -57.363 5.14e-18 -14.811
HMC_vs_DEMetro_Z 4 -33.666 8.48e-15 -8.693
HMC_vs_DEMetro_Z 5 -40.645 6.22e-16 -10.494
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.068 0.013 0.005 11.611
HMC 4 0.056 0.013 0.005 7.881
HMC 6 0.066 0.014 0.004 11.770
HMC 8 0.069 0.012 0.003 18.783
HMC 10 0.107 0.014 0.005 19.167
HMC 12 0.094 0.014 0.004 17.931
SMC 0 0.016 0.013 0.005 0.535
SMC 4 0.013 0.013 0.005 0.003
SMC 6 0.015 0.014 0.004 0.257
SMC 8 0.013 0.012 0.003 0.464
SMC 10 0.015 0.014 0.005 0.226
SMC 12 0.014 0.014 0.004 -0.023
Metro 0 0.324 0.013 0.005 65.605
Metro 4 0.266 0.013 0.005 46.776
Metro 6 0.320 0.014 0.004 69.249
Metro 8 0.276 0.012 0.003 86.562
Metro 10 0.215 0.014 0.005 41.617
Metro 12 0.289 0.014 0.004 62.035
DEMetro_Z 0 0.562 0.013 0.005 116.055
DEMetro_Z 4 0.568 0.013 0.005 102.637
DEMetro_Z 6 0.572 0.014 0.004 126.345
DEMetro_Z 8 0.577 0.012 0.003 185.041
DEMetro_Z 10 0.589 0.014 0.005 118.723
DEMetro_Z 12 0.568 0.014 0.004 125.108
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.886 0.0117 5.784
HMC 4 4.571 0.000411 10.744
HMC 6 4.914 0.000207 9.894
HMC 8 8.345 6.4e-07 15.751
HMC 10 18.638 5.69e-12 22.193
HMC 12 33.051 6.15e-20 17.961
SMC 0 1.362 0.184 0.546
SMC 4 0.252 0.803 0.108
SMC 6 1.038 0.31 0.502
SMC 8 -1.510 0.142 -0.532
SMC 10 1.952 0.0619 0.858
SMC 12 -1.017 0.32 -0.300
Metro 0 4.316 0.00071 85.483
Metro 4 3.757 0.00212 32.598
Metro 6 5.354 0.000101 57.492
Metro 8 4.013 0.00128 54.848
Metro 10 2.837 0.0132 40.562
Metro 12 5.985 3.32e-05 53.420
DEMetro_Z 0 24.893 5.43e-13 1151.768
DEMetro_Z 4 21.596 3.79e-12 979.900
DEMetro_Z 6 27.212 1.6e-13 1093.448
DEMetro_Z 8 29.384 5.54e-14 944.210
DEMetro_Z 10 27.707 1.25e-13 1115.958
DEMetro_Z 12 30.956 2.69e-14 770.862
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -24.569 6.5e-13 -6.344
HMC_vs_DEMetro_Z 1 -21.039 5.41e-12 -5.432
HMC_vs_DEMetro_Z 2 -27.109 1.68e-13 -7.000
HMC_vs_DEMetro_Z 3 -27.980 1.09e-13 -7.224
HMC_vs_DEMetro_Z 4 -27.023 1.76e-13 -6.977
HMC_vs_DEMetro_Z 5 -30.392 3.49e-14 -7.847
Metro_vs_SMC 0 4.302 0.00073 1.111
Metro_vs_SMC 1 3.726 0.00226 0.962
Metro_vs_SMC 2 5.383 9.66e-05 1.390
Metro_vs_SMC 3 4.038 0.00122 1.043
Metro_vs_SMC 4 2.805 0.014 0.724
Metro_vs_SMC 5 5.995 3.29e-05 1.548
Metro_vs_DEMetro_Z 0 -23.103 1.51e-12 -5.965
Metro_vs_DEMetro_Z 1 -20.351 8.49e-12 -5.255
Metro_vs_DEMetro_Z 2 -22.330 2.4e-12 -5.766
Metro_vs_DEMetro_Z 3 -23.057 1.55e-12 -5.953
Metro_vs_DEMetro_Z 4 -25.211 4.57e-13 -6.509
Metro_vs_DEMetro_Z 5 -24.873 5.49e-13 -6.422
HMC_vs_Metro 0 -4.025 0.00125 -1.039
HMC_vs_Metro 1 -2.203 0.0449 -0.569
HMC_vs_Metro 2 -4.738 0.000318 -1.223
HMC_vs_Metro 3 -2.930 0.011 -0.757
HMC_vs_Metro 4 -1.269 0.225 -0.328
HMC_vs_Metro 5 -3.920 0.00154 -1.012
HMC_vs_SMC 0 2.691 0.0176 0.695
HMC_vs_SMC 1 4.532 0.000469 1.170
HMC_vs_SMC 2 4.764 0.000302 1.230
HMC_vs_SMC 3 8.331 8.51e-07 2.151
HMC_vs_SMC 4 17.228 8.04e-11 4.448
HMC_vs_SMC 5 39.746 8.49e-16 10.262
DEMetro_Z_vs_SMC 0 24.939 5.3e-13 6.439
DEMetro_Z_vs_SMC 1 21.596 3.79e-12 5.576
DEMetro_Z_vs_SMC 2 27.176 1.63e-13 7.017
DEMetro_Z_vs_SMC 3 29.464 5.35e-14 7.607
DEMetro_Z_vs_SMC 4 27.744 1.23e-13 7.163
DEMetro_Z_vs_SMC 5 31.018 2.63e-14 8.009
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.069 0.016 0.009 5.784
HMC 4 0.127 0.016 0.010 10.744
HMC 6 0.116 0.019 0.010 9.894
HMC 8 0.193 0.020 0.011 15.751
HMC 10 0.244 0.017 0.010 22.193
HMC 12 0.263 0.023 0.013 17.961
SMC 0 0.021 0.016 0.009 0.546
SMC 4 0.017 0.016 0.010 0.108
SMC 6 0.024 0.019 0.010 0.502
SMC 8 0.014 0.020 0.011 -0.532
SMC 10 0.026 0.017 0.010 0.858
SMC 12 0.019 0.023 0.013 -0.300
Metro 0 0.805 0.016 0.009 85.483
Metro 4 0.354 0.016 0.010 32.598
Metro 6 0.580 0.019 0.010 57.492
Metro 8 0.625 0.020 0.011 54.848
Metro 10 0.431 0.017 0.010 40.562
Metro 12 0.736 0.023 0.013 53.420
DEMetro_Z 0 10.650 0.016 0.009 1151.768
DEMetro_Z 4 10.174 0.016 0.010 979.900
DEMetro_Z 6 10.695 0.019 0.010 1093.448
DEMetro_Z 8 10.443 0.020 0.011 944.210
DEMetro_Z 10 11.386 0.017 0.010 1115.958
DEMetro_Z 12 10.321 0.023 0.013 770.862
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 5.020 0.000155 7.292
HMC 4 3.029 0.00872 5.894
HMC 6 4.032 0.00104 4.763
HMC 8 8.589 5.23e-07 23.974
HMC 10 22.685 2.87e-14 18.134
HMC 12 41.207 2.85e-21 23.777
SMC 0 -1.128 0.27 -0.352
SMC 4 0.871 0.392 0.363
SMC 6 -0.396 0.695 -0.156
SMC 8 1.616 0.125 1.410
SMC 10 -1.744 0.0926 -0.584
SMC 12 0.803 0.429 0.265
Metro 0 11.333 1.58e-08 29.525
Metro 4 7.831 1.58e-06 22.806
Metro 6 8.184 9.74e-07 28.829
Metro 8 7.907 1.55e-06 78.448
Metro 10 6.212 2.22e-05 32.585
Metro 12 6.600 1.16e-05 34.241
DEMetro_Z 0 14.759 6.3e-10 1116.848
DEMetro_Z 4 11.673 1.33e-08 1422.051
DEMetro_Z 6 10.301 6.46e-08 925.323
DEMetro_Z 8 9.677 1.4e-07 3560.808
DEMetro_Z 10 11.664 1.35e-08 1872.553
DEMetro_Z 12 10.274 6.67e-08 1362.860
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 5.321 0.000108 1.374
HMC_vs_SMC 1 2.737 0.0161 0.707
HMC_vs_SMC 2 4.295 0.000741 1.109
HMC_vs_SMC 3 7.412 3.29e-06 1.914
HMC_vs_SMC 4 23.681 1.08e-12 6.114
HMC_vs_SMC 5 40.777 5.95e-16 10.529
Metro_vs_DEMetro_Z 0 -14.223 1.03e-09 -3.672
Metro_vs_DEMetro_Z 1 -11.484 1.64e-08 -2.965
Metro_vs_DEMetro_Z 2 -9.788 1.22e-07 -2.527
Metro_vs_DEMetro_Z 3 -9.495 1.77e-07 -2.452
Metro_vs_DEMetro_Z 4 -11.385 1.83e-08 -2.940
Metro_vs_DEMetro_Z 5 -9.989 9.47e-08 -2.579
HMC_vs_Metro 0 -6.943 6.83e-06 -1.793
HMC_vs_Metro 1 -4.378 0.00063 -1.131
HMC_vs_Metro 2 -6.630 1.13e-05 -1.712
HMC_vs_Metro 3 -4.698 0.000342 -1.213
HMC_vs_Metro 4 -2.869 0.0124 -0.741
HMC_vs_Metro 5 -2.008 0.0644 -0.518
HMC_vs_DEMetro_Z 0 -14.879 5.66e-10 -3.842
HMC_vs_DEMetro_Z 1 -11.584 1.47e-08 -2.991
HMC_vs_DEMetro_Z 2 -10.267 6.73e-08 -2.651
HMC_vs_DEMetro_Z 3 -9.611 1.52e-07 -2.482
HMC_vs_DEMetro_Z 4 -11.561 1.51e-08 -2.985
HMC_vs_DEMetro_Z 5 -10.114 8.12e-08 -2.611
Metro_vs_SMC 0 11.425 1.75e-08 2.950
Metro_vs_SMC 1 7.532 2.74e-06 1.945
Metro_vs_SMC 2 7.968 1.43e-06 2.057
Metro_vs_SMC 3 7.843 1.72e-06 2.025
Metro_vs_SMC 4 6.382 1.71e-05 1.648
Metro_vs_SMC 5 6.553 1.29e-05 1.692
DEMetro_Z_vs_SMC 0 14.761 6.29e-10 3.811
DEMetro_Z_vs_SMC 1 11.677 1.33e-08 3.015
DEMetro_Z_vs_SMC 2 10.317 6.33e-08 2.664
DEMetro_Z_vs_SMC 3 9.675 1.4e-07 2.498
DEMetro_Z_vs_SMC 4 11.666 1.34e-08 3.012
DEMetro_Z_vs_SMC 5 10.271 6.7e-08 2.652
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.153 0.029 0.017 7.292
HMC 4 0.109 0.024 0.014 5.894
HMC 6 0.132 0.036 0.020 4.763
HMC 8 0.161 0.019 0.006 23.974
HMC 10 0.257 0.031 0.012 18.134
HMC 12 0.362 0.028 0.014 23.777
SMC 0 0.023 0.029 0.017 -0.352
SMC 4 0.029 0.024 0.014 0.363
SMC 6 0.033 0.036 0.020 -0.156
SMC 8 0.028 0.019 0.006 1.410
SMC 10 0.023 0.031 0.012 -0.584
SMC 12 0.032 0.028 0.014 0.265
Metro 0 0.533 0.029 0.017 29.525
Metro 4 0.353 0.024 0.014 22.806
Metro 6 0.614 0.036 0.020 28.829
Metro 8 0.483 0.019 0.006 78.448
Metro 10 0.438 0.031 0.012 32.585
Metro 12 0.509 0.028 0.014 34.241
DEMetro_Z 0 19.081 0.029 0.017 1116.848
DEMetro_Z 4 20.544 0.024 0.014 1422.051
DEMetro_Z 6 18.564 0.036 0.020 925.323
DEMetro_Z 8 21.049 0.019 0.006 3560.808
DEMetro_Z 10 23.430 0.031 0.012 1872.553
DEMetro_Z 12 19.159 0.028 0.014 1362.860
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 5.508 6.97e-05 12.008
HMC 4 5.470 7.81e-05 15.992
HMC 6 6.200 2.07e-05 14.399
HMC 8 8.946 3.21e-07 25.579
HMC 10 18.071 2.3e-11 34.094
HMC 12 28.755 1.99e-15 26.633
SMC 0 0.958 0.346 0.349
SMC 4 0.670 0.509 0.276
SMC 6 0.563 0.579 0.268
SMC 8 -0.476 0.638 -0.179
SMC 10 1.357 0.187 0.652
SMC 12 -1.504 0.148 -0.429
Metro 0 4.869 0.000248 120.465
Metro 4 5.355 0.000101 54.159
Metro 6 6.537 1.31e-05 85.146
Metro 8 4.522 0.000479 89.988
Metro 10 3.896 0.00161 75.470
Metro 12 6.928 6.97e-06 83.890
DEMetro_Z 0 26.614 2.17e-13 1620.205
DEMetro_Z 4 19.428 1.59e-11 1369.785
DEMetro_Z 6 29.553 5.12e-14 1481.221
DEMetro_Z 8 29.207 6.03e-14 1522.925
DEMetro_Z 10 27.793 1.2e-13 1775.324
DEMetro_Z 12 32.692 1.27e-14 1174.376
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -26.347 2.49e-13 -6.803
Metro_vs_DEMetro_Z 1 -18.217 3.8e-11 -4.704
Metro_vs_DEMetro_Z 2 -24.752 5.87e-13 -6.391
Metro_vs_DEMetro_Z 3 -23.795 1.01e-12 -6.144
Metro_vs_DEMetro_Z 4 -24.870 5.5e-13 -6.421
Metro_vs_DEMetro_Z 5 -27.557 1.34e-13 -7.115
DEMetro_Z_vs_SMC 0 26.655 2.13e-13 6.882
DEMetro_Z_vs_SMC 1 19.431 1.59e-11 5.017
DEMetro_Z_vs_SMC 2 29.545 5.15e-14 7.628
DEMetro_Z_vs_SMC 3 29.223 5.99e-14 7.545
DEMetro_Z_vs_SMC 4 27.816 1.18e-13 7.182
DEMetro_Z_vs_SMC 5 32.718 1.26e-14 8.448
HMC_vs_DEMetro_Z 0 -26.515 2.29e-13 -6.846
HMC_vs_DEMetro_Z 1 -18.913 2.29e-11 -4.883
HMC_vs_DEMetro_Z 2 -29.726 4.73e-14 -7.675
HMC_vs_DEMetro_Z 3 -28.014 1.07e-13 -7.233
HMC_vs_DEMetro_Z 4 -27.052 1.74e-13 -6.985
HMC_vs_DEMetro_Z 5 -32.254 1.53e-14 -8.328
HMC_vs_Metro 0 -4.377 0.000632 -1.130
HMC_vs_Metro 1 -3.310 0.00516 -0.855
HMC_vs_Metro 2 -5.723 5.26e-05 -1.478
HMC_vs_Metro 3 -3.333 0.00493 -0.861
HMC_vs_Metro 4 -2.083 0.0561 -0.538
HMC_vs_Metro 5 -4.689 0.000349 -1.211
HMC_vs_SMC 0 5.531 7.4e-05 1.428
HMC_vs_SMC 1 5.292 0.000114 1.366
HMC_vs_SMC 2 6.182 2.39e-05 1.596
HMC_vs_SMC 3 8.765 4.66e-07 2.263
HMC_vs_SMC 4 17.271 7.78e-11 4.459
HMC_vs_SMC 5 32.311 1.5e-14 8.343
Metro_vs_SMC 0 4.866 0.00025 1.256
Metro_vs_SMC 1 5.302 0.000112 1.369
Metro_vs_SMC 2 6.584 1.22e-05 1.700
Metro_vs_SMC 3 4.526 0.000475 1.169
Metro_vs_SMC 4 3.904 0.00159 1.008
Metro_vs_SMC 5 6.945 6.82e-06 1.793
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.087 0.022 0.005 12.008
HMC 4 0.122 0.022 0.006 15.992
HMC 6 0.112 0.026 0.006 14.399
HMC 8 0.170 0.023 0.006 25.579
HMC 10 0.205 0.024 0.005 34.094
HMC 12 0.218 0.027 0.007 26.633
SMC 0 0.024 0.022 0.005 0.349
SMC 4 0.024 0.022 0.006 0.276
SMC 6 0.027 0.026 0.006 0.268
SMC 8 0.022 0.023 0.006 -0.179
SMC 10 0.028 0.024 0.005 0.652
SMC 12 0.024 0.027 0.007 -0.429
Metro 0 0.670 0.022 0.005 120.465
Metro 4 0.360 0.022 0.006 54.159
Metro 6 0.533 0.026 0.006 85.146
Metro 8 0.541 0.023 0.006 89.988
Metro 10 0.425 0.024 0.005 75.470
Metro 12 0.630 0.027 0.007 83.890
DEMetro_Z 0 8.739 0.022 0.005 1620.205
DEMetro_Z 4 8.565 0.022 0.006 1369.785
DEMetro_Z 6 8.847 0.026 0.006 1481.221
DEMetro_Z 8 8.789 0.023 0.006 1522.925
DEMetro_Z 10 9.463 0.024 0.005 1775.324
DEMetro_Z 12 8.467 0.027 0.007 1174.376
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 6.259 1.62e-05 9.561
HMC 4 5.403 8.46e-05 11.928
HMC 6 6.404 1.37e-05 12.022
HMC 8 11.393 1.55e-08 34.081
HMC 10 31.052 8.24e-16 30.144
HMC 12 39.036 2.14e-17 37.861
SMC 0 -0.075 0.941 -0.026
SMC 4 0.669 0.509 0.247
SMC 6 0.573 0.571 0.256
SMC 8 0.830 0.414 0.379
SMC 10 0.917 0.367 0.363
SMC 12 -0.655 0.519 -0.210
Metro 0 5.928 3.67e-05 87.960
Metro 4 6.991 6.2e-06 41.099
Metro 6 11.255 2.06e-08 76.806
Metro 8 5.676 5.72e-05 104.214
Metro 10 4.923 0.000224 53.619
Metro 12 7.240 4.27e-06 82.069
DEMetro_Z 0 41.560 3.92e-16 203.206
DEMetro_Z 4 63.239 6.83e-19 164.449
DEMetro_Z 6 40.697 5.35e-16 211.949
DEMetro_Z 8 35.354 4.12e-15 309.734
DEMetro_Z 10 69.406 1.97e-19 191.780
DEMetro_Z 12 74.598 6.98e-20 204.559
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 41.602 4.5e-16 10.742
DEMetro_Z_vs_SMC 1 63.087 1.36e-18 16.289
DEMetro_Z_vs_SMC 2 41.072 5.38e-16 10.605
DEMetro_Z_vs_SMC 3 35.789 3.64e-15 9.241
DEMetro_Z_vs_SMC 4 69.174 3.77e-19 17.861
DEMetro_Z_vs_SMC 5 74.974 1.23e-19 19.358
HMC_vs_Metro 0 -5.265 0.000119 -1.360
HMC_vs_Metro 1 -4.173 0.000939 -1.077
HMC_vs_Metro 2 -9.306 2.26e-07 -2.403
HMC_vs_Metro 3 -4.065 0.00116 -1.050
HMC_vs_Metro 4 -2.136 0.0508 -0.552
HMC_vs_Metro 5 -3.841 0.0018 -0.992
Metro_vs_DEMetro_Z 0 -7.248 4.24e-06 -1.871
Metro_vs_DEMetro_Z 1 -18.965 2.21e-11 -4.897
Metro_vs_DEMetro_Z 2 -14.044 1.21e-09 -3.626
Metro_vs_DEMetro_Z 3 -8.876 4e-07 -2.292
Metro_vs_DEMetro_Z 4 -12.992 3.35e-09 -3.354
Metro_vs_DEMetro_Z 5 -9.744 1.29e-07 -2.516
HMC_vs_SMC 0 6.255 2.11e-05 1.615
HMC_vs_SMC 1 5.358 0.000101 1.383
HMC_vs_SMC 2 6.114 2.68e-05 1.579
HMC_vs_SMC 3 10.885 3.23e-08 2.811
HMC_vs_SMC 4 32.501 1.38e-14 8.392
HMC_vs_SMC 5 44.770 1.62e-16 11.559
Metro_vs_SMC 0 5.967 3.45e-05 1.541
Metro_vs_SMC 1 6.900 7.33e-06 1.782
Metro_vs_SMC 2 11.317 1.98e-08 2.922
Metro_vs_SMC 3 5.672 5.76e-05 1.465
Metro_vs_SMC 4 4.972 0.000205 1.284
Metro_vs_SMC 5 7.218 4.44e-06 1.864
HMC_vs_DEMetro_Z 0 -36.056 3.28e-15 -9.310
HMC_vs_DEMetro_Z 1 -43.450 2.46e-16 -11.219
HMC_vs_DEMetro_Z 2 -36.161 3.15e-15 -9.337
HMC_vs_DEMetro_Z 3 -26.341 2.5e-13 -6.801
HMC_vs_DEMetro_Z 4 -58.558 3.86e-18 -15.120
HMC_vs_DEMetro_Z 5 -64.525 9.96e-19 -16.660
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.059 0.013 0.005 9.561
HMC 4 0.078 0.013 0.005 11.928
HMC 6 0.067 0.014 0.004 12.022
HMC 8 0.116 0.012 0.003 34.081
HMC 10 0.160 0.014 0.005 30.144
HMC 12 0.182 0.014 0.004 37.861
SMC 0 0.013 0.013 0.005 -0.026
SMC 4 0.014 0.013 0.005 0.247
SMC 6 0.015 0.014 0.004 0.256
SMC 8 0.013 0.012 0.003 0.379
SMC 10 0.016 0.014 0.005 0.363
SMC 12 0.013 0.014 0.004 -0.210
Metro 0 0.429 0.013 0.005 87.960
Metro 4 0.235 0.013 0.005 41.099
Metro 6 0.353 0.014 0.004 76.806
Metro 8 0.330 0.012 0.003 104.214
Metro 10 0.274 0.014 0.005 53.619
Metro 12 0.378 0.014 0.004 82.069
DEMetro_Z 0 0.974 0.013 0.005 203.206
DEMetro_Z 4 0.902 0.013 0.005 164.449
DEMetro_Z 6 0.950 0.014 0.004 211.949
DEMetro_Z 8 0.958 0.012 0.003 309.734
DEMetro_Z 10 0.943 0.014 0.005 191.780
DEMetro_Z 12 0.920 0.014 0.004 204.559
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

Varying_Mode_Distance_with_Dim_and_Tails (Mixture, mm, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.983 0.00848 2.602
HMC 4 2.568 0.0222 10.140
HMC 6 3.024 0.0073 2.199
HMC 8 3.205 0.00368 1.455
HMC 10 1.274 0.224 45.319
HMC 12 5.431 8.76e-05 36.480
SMC 0 31.820 3.25e-15 43.342
SMC 4 26.524 2.07e-13 144.529
SMC 6 25.296 1.54e-13 41.310
SMC 8 45.456 6.51e-17 106.300
SMC 10 29.077 5.04e-14 102.304
SMC 12 35.389 3.92e-15 228.653
Metro 0 6.614 7.35e-06 7.968
Metro 4 8.109 1.06e-06 24.280
Metro 6 6.655 4.38e-06 5.721
Metro 8 7.779 1.26e-06 11.248
Metro 10 3.599 0.00289 23.434
Metro 12 8.384 7.34e-07 30.201
DEMetro_Z 0 20.693 6.67e-12 257.319
DEMetro_Z 4 19.654 1.36e-11 574.250
DEMetro_Z 6 18.477 3.08e-11 198.489
DEMetro_Z 8 16.988 9.66e-11 381.657
DEMetro_Z 10 21.107 5.15e-12 486.535
DEMetro_Z 12 15.979 2.2e-10 926.826
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -21.057 5.35e-12 -5.437
HMC_vs_DEMetro_Z 1 -20.164 9.63e-12 -5.206
HMC_vs_DEMetro_Z 2 -18.400 3.32e-11 -4.751
HMC_vs_DEMetro_Z 3 -16.858 1.08e-10 -4.353
HMC_vs_DEMetro_Z 4 -12.081 8.58e-09 -3.119
HMC_vs_DEMetro_Z 5 -15.028 4.97e-10 -3.880
Metro_vs_SMC 0 -17.696 5.61e-11 -4.569
Metro_vs_SMC 1 -21.256 4.7e-12 -5.488
Metro_vs_SMC 2 -17.787 5.24e-11 -4.593
Metro_vs_SMC 3 -57.257 5.28e-18 -14.784
Metro_vs_SMC 4 -10.034 8.96e-08 -2.591
Metro_vs_SMC 5 -30.664 3.08e-14 -7.917
Metro_vs_DEMetro_Z 0 -19.804 1.23e-11 -5.113
Metro_vs_DEMetro_Z 1 -18.263 3.67e-11 -4.716
Metro_vs_DEMetro_Z 2 -18.276 3.64e-11 -4.719
Metro_vs_DEMetro_Z 3 -16.236 1.78e-10 -4.192
Metro_vs_DEMetro_Z 4 -21.791 3.35e-12 -5.626
Metro_vs_DEMetro_Z 5 -15.409 3.56e-10 -3.979
HMC_vs_Metro 0 -3.976 0.00138 -1.027
HMC_vs_Metro 1 -2.917 0.0112 -0.753
HMC_vs_Metro 2 -4.287 0.000752 -1.107
HMC_vs_Metro 3 -7.611 2.43e-06 -1.965
HMC_vs_Metro 4 0.719 0.484 0.186
HMC_vs_Metro 5 1.079 0.299 0.279
HMC_vs_SMC 0 -25.478 3.95e-13 -6.578
HMC_vs_SMC 1 -18.418 3.28e-11 -4.756
HMC_vs_SMC 2 -25.277 4.41e-13 -6.527
HMC_vs_SMC 3 -48.669 5.08e-17 -12.566
HMC_vs_SMC 4 -1.566 0.14 -0.404
HMC_vs_SMC 5 -19.734 1.29e-11 -5.095
DEMetro_Z_vs_SMC 0 17.749 5.39e-11 4.583
DEMetro_Z_vs_SMC 1 15.775 2.61e-10 4.073
DEMetro_Z_vs_SMC 2 14.763 6.28e-10 3.812
DEMetro_Z_vs_SMC 3 11.810 1.15e-08 3.049
DEMetro_Z_vs_SMC 4 17.447 6.79e-11 4.505
DEMetro_Z_vs_SMC 5 11.795 1.17e-08 3.045
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.117 0.071 0.017 2.602
HMC 4 0.153 0.062 0.009 10.140
HMC 6 0.123 0.067 0.026 2.199
HMC 8 0.160 0.084 0.052 1.455
HMC 10 0.579 0.070 0.011 45.319
HMC 12 0.392 0.066 0.009 36.480
SMC 0 0.828 0.071 0.017 43.342
SMC 4 1.360 0.062 0.009 144.529
SMC 6 1.128 0.067 0.026 41.310
SMC 8 5.660 0.084 0.052 106.300
SMC 10 1.220 0.070 0.011 102.304
SMC 12 2.112 0.066 0.009 228.653
Metro 0 0.210 0.071 0.017 7.968
Metro 4 0.280 0.062 0.009 24.280
Metro 6 0.214 0.067 0.026 5.721
Metro 8 0.674 0.084 0.052 11.248
Metro 10 0.333 0.070 0.011 23.434
Metro 12 0.336 0.066 0.009 30.201
DEMetro_Z 0 4.564 0.071 0.017 257.319
DEMetro_Z 4 5.218 0.062 0.009 574.250
DEMetro_Z 6 5.164 0.067 0.026 198.489
DEMetro_Z 8 20.105 0.084 0.052 381.657
DEMetro_Z 10 5.540 0.070 0.011 486.535
DEMetro_Z 12 8.359 0.066 0.009 926.826
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.082 0.294 0.899
HMC 4 2.115 0.0526 6.628
HMC 6 0.376 0.71 0.116
HMC 8 -1.090 0.293 -0.284
HMC 10 0.999 0.335 267.262
HMC 12 0.544 0.592 0.270
SMC 0 130.117 3.68e-25 142.590
SMC 4 152.540 4.18e-24 632.671
SMC 6 235.098 1.05e-31 186.795
SMC 8 80.854 3.12e-22 82.429
SMC 10 288.364 1.19e-31 269.581
SMC 12 141.218 2.53e-25 169.870
Metro 0 1.022 0.32 0.726
Metro 4 3.125 0.0073 8.009
Metro 6 1.424 0.169 0.769
Metro 8 1.727 0.0953 0.605
Metro 10 1.295 0.216 6.462
Metro 12 1.281 0.219 1.563
DEMetro_Z 0 14.588 4.55e-10 28.256
DEMetro_Z 4 14.851 5.68e-10 136.206
DEMetro_Z 6 10.765 3.42e-08 42.223
DEMetro_Z 8 10.763 3.53e-08 51.686
DEMetro_Z 10 8.980 3.4e-07 60.107
DEMetro_Z 12 9.761 1.2e-07 47.922
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -102.129 1.63e-21 -26.370
HMC_vs_SMC 1 -102.984 1.45e-21 -26.590
HMC_vs_SMC 2 -230.208 1.88e-26 -59.440
HMC_vs_SMC 3 -83.227 2.85e-20 -21.489
HMC_vs_SMC 4 -0.009 0.993 -0.002
HMC_vs_SMC 5 -123.362 1.16e-22 -31.852
Metro_vs_DEMetro_Z 0 -12.107 8.34e-09 -3.126
Metro_vs_DEMetro_Z 1 -12.403 6.11e-09 -3.202
Metro_vs_DEMetro_Z 2 -10.520 4.97e-08 -2.716
Metro_vs_DEMetro_Z 3 -10.606 4.48e-08 -2.739
Metro_vs_DEMetro_Z 4 -6.741 9.46e-06 -1.740
Metro_vs_DEMetro_Z 5 -9.317 2.23e-07 -2.406
HMC_vs_Metro 0 0.458 0.654 0.118
HMC_vs_Metro 1 -0.351 0.731 -0.091
HMC_vs_Metro 2 -1.244 0.234 -0.321
HMC_vs_Metro 3 -3.599 0.0029 -0.929
HMC_vs_Metro 4 0.993 0.338 0.256
HMC_vs_Metro 5 -1.113 0.284 -0.287
HMC_vs_DEMetro_Z 0 -11.654 1.36e-08 -3.009
HMC_vs_DEMetro_Z 1 -13.772 1.57e-09 -3.556
HMC_vs_DEMetro_Z 2 -10.727 3.89e-08 -2.770
HMC_vs_DEMetro_Z 3 -10.854 3.36e-08 -2.802
HMC_vs_DEMetro_Z 4 0.776 0.451 0.200
HMC_vs_DEMetro_Z 5 -9.987 9.49e-08 -2.579
Metro_vs_SMC 0 -104.340 1.21e-21 -26.940
Metro_vs_SMC 1 -144.675 1.25e-23 -37.355
Metro_vs_SMC 2 -224.021 2.75e-26 -57.842
Metro_vs_SMC 3 -88.150 1.28e-20 -22.760
Metro_vs_SMC 4 -52.947 1.57e-17 -13.671
Metro_vs_SMC 5 -86.519 1.66e-20 -22.339
DEMetro_Z_vs_SMC 0 -50.031 3.46e-17 -12.918
DEMetro_Z_vs_SMC 1 -49.330 4.21e-17 -12.737
DEMetro_Z_vs_SMC 2 -39.397 9.59e-16 -10.172
DEMetro_Z_vs_SMC 3 -6.348 1.8e-05 -1.639
DEMetro_Z_vs_SMC 4 -31.093 2.55e-14 -8.028
DEMetro_Z_vs_SMC 5 -23.293 1.35e-12 -6.014
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 19.337 11.222 9.030 0.899
HMC 4 23.655 3.824 2.992 6.628
HMC 6 7.215 6.080 9.746 0.116
HMC 8 10.498 40.803 106.713 -0.284
HMC 10 1802.822 7.004 6.719 267.262
HMC 12 14.933 9.345 20.708 0.270
SMC 0 1298.739 11.222 9.030 142.590
SMC 4 1896.885 3.824 2.992 632.671
SMC 6 1826.505 6.080 9.746 186.795
SMC 8 8837.044 40.803 106.713 82.429
SMC 10 1818.407 7.004 6.719 269.581
SMC 12 3527.079 9.345 20.708 169.870
Metro 0 17.775 11.222 9.030 0.726
Metro 4 27.787 3.824 2.992 8.009
Metro 6 13.571 6.080 9.746 0.769
Metro 8 105.336 40.803 106.713 0.605
Metro 10 50.424 7.004 6.719 6.462
Metro 12 41.710 9.345 20.708 1.563
DEMetro_Z 0 266.357 11.222 9.030 28.256
DEMetro_Z 4 411.374 3.824 2.992 136.206
DEMetro_Z 6 417.569 6.080 9.746 42.223
DEMetro_Z 8 5556.350 40.803 106.713 51.686
DEMetro_Z 10 410.886 7.004 6.719 60.107
DEMetro_Z 12 1001.725 9.345 20.708 47.922
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 3.297 0.00526 15.624
HMC 4 2.594 0.0212 62.396
HMC 6 3.071 0.00822 12.034
HMC 8 3.752 0.0019 4.951
HMC 10 1.049 0.312 233.599
HMC 12 5.387 9.37e-05 24.088
SMC 0 241.105 7.96e-27 1381.841
SMC 4 293.875 5.71e-28 2895.802
SMC 6 459.018 4.52e-31 1328.506
SMC 8 170.801 1.1e-24 1301.863
SMC 10 598.736 1.22e-32 1893.074
SMC 12 290.373 6.46e-28 2260.339
Metro 0 3.656 0.00259 32.112
Metro 4 5.378 9.73e-05 101.751
Metro 6 3.676 0.00248 33.617
Metro 8 6.809 8.42e-06 71.978
Metro 10 2.966 0.0102 72.048
Metro 12 2.735 0.0161 62.113
DEMetro_Z 0 31.245 2.36e-14 561.512
DEMetro_Z 4 28.684 7.73e-14 1232.998
DEMetro_Z 6 21.565 3.85e-12 568.125
DEMetro_Z 8 22.443 2.24e-12 982.142
DEMetro_Z 10 21.618 3.73e-12 811.674
DEMetro_Z 12 19.712 1.31e-11 1103.118
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -25.043 5.01e-13 -6.466
Metro_vs_DEMetro_Z 1 -22.329 2.4e-12 -5.765
Metro_vs_DEMetro_Z 2 -20.059 1.03e-11 -5.179
Metro_vs_DEMetro_Z 3 -19.551 1.46e-11 -5.048
Metro_vs_DEMetro_Z 4 -19.794 1.24e-11 -5.111
Metro_vs_DEMetro_Z 5 -17.131 8.68e-11 -4.423
DEMetro_Z_vs_SMC 0 -41.283 5.01e-16 -10.659
DEMetro_Z_vs_SMC 1 -37.298 2.05e-15 -9.630
DEMetro_Z_vs_SMC 2 -29.851 4.47e-14 -7.708
DEMetro_Z_vs_SMC 3 -7.300 3.91e-06 -1.885
DEMetro_Z_vs_SMC 4 -28.620 7.99e-14 -7.390
DEMetro_Z_vs_SMC 5 -20.303 8.77e-12 -5.242
HMC_vs_DEMetro_Z 0 -32.027 1.69e-14 -8.269
HMC_vs_DEMetro_Z 1 -27.080 1.71e-13 -6.992
HMC_vs_DEMetro_Z 2 -21.937 3.06e-12 -5.664
HMC_vs_DEMetro_Z 3 -22.207 2.59e-12 -5.734
HMC_vs_DEMetro_Z 4 -2.650 0.019 -0.684
HMC_vs_DEMetro_Z 5 -19.145 1.94e-11 -4.943
HMC_vs_Metro 0 -1.597 0.133 -0.412
HMC_vs_Metro 1 -1.432 0.174 -0.370
HMC_vs_Metro 2 -2.165 0.0481 -0.559
HMC_vs_Metro 3 -6.074 2.87e-05 -1.568
HMC_vs_Metro 4 0.807 0.433 0.208
HMC_vs_Metro 5 -1.748 0.102 -0.451
HMC_vs_SMC 0 -172.209 1.09e-24 -44.464
HMC_vs_SMC 1 -98.267 2.79e-21 -25.372
HMC_vs_SMC 2 -281.384 1.13e-27 -72.653
HMC_vs_SMC 3 -157.332 3.86e-24 -40.623
HMC_vs_SMC 4 -7.472 3.01e-06 -1.929
HMC_vs_SMC 5 -229.067 2.01e-26 -59.145
Metro_vs_SMC 0 -138.045 2.41e-23 -35.643
Metro_vs_SMC 1 -132.301 4.36e-23 -34.160
Metro_vs_SMC 2 -135.704 3.06e-23 -35.039
Metro_vs_SMC 3 -129.492 5.89e-23 -33.435
Metro_vs_SMC 4 -73.947 1.49e-19 -19.093
Metro_vs_SMC 5 -88.616 1.19e-20 -22.881
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.433 0.124 0.020 15.624
HMC 4 0.825 0.110 0.011 62.396
HMC 6 0.409 0.115 0.024 12.034
HMC 8 0.408 0.137 0.055 4.951
HMC 10 4.105 0.122 0.017 233.599
HMC 12 0.602 0.121 0.020 24.088
SMC 0 27.433 0.124 0.020 1381.841
SMC 4 33.316 0.110 0.011 2895.802
SMC 6 32.577 0.115 0.024 1328.506
SMC 8 71.475 0.137 0.055 1301.863
SMC 10 32.397 0.122 0.017 1893.074
SMC 12 45.274 0.121 0.020 2260.339
Metro 0 0.758 0.124 0.020 32.112
Metro 4 1.277 0.110 0.011 101.751
Metro 6 0.937 0.115 0.024 33.617
Metro 8 4.081 0.137 0.055 71.978
Metro 10 1.351 0.122 0.017 72.048
Metro 12 1.362 0.121 0.020 62.113
DEMetro_Z 0 11.221 0.124 0.020 561.512
DEMetro_Z 4 14.249 0.110 0.011 1232.998
DEMetro_Z 6 13.997 0.115 0.024 568.125
DEMetro_Z 8 53.955 0.137 0.055 982.142
DEMetro_Z 10 13.960 0.122 0.017 811.674
DEMetro_Z 12 22.157 0.121 0.020 1103.118
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.364 0.000644 31.330
HMC 4 4.109 0.00106 75.739
HMC 6 3.665 0.00254 50.884
HMC 8 5.156 0.000145 36.414
HMC 10 4.277 0.000765 41.195
HMC 12 7.893 1.59e-06 87.083
SMC 0 130.544 4.71e-24 203.948
SMC 4 162.320 4.47e-25 309.718
SMC 6 133.791 1.47e-23 336.140
SMC 8 145.237 1.09e-24 232.310
SMC 10 137.379 4.23e-24 249.384
SMC 12 165.097 2.58e-25 290.966
Metro 0 6.200 2.29e-05 47.668
Metro 4 8.001 1.36e-06 115.968
Metro 6 5.560 7.02e-05 108.037
Metro 8 14.274 9.7e-10 193.752
Metro 10 6.677 1.04e-05 88.555
Metro 12 6.316 1.9e-05 115.516
DEMetro_Z 0 74.642 8.44e-20 246.507
DEMetro_Z 4 47.764 6.17e-17 367.656
DEMetro_Z 6 54.077 1.09e-17 403.902
DEMetro_Z 8 49.159 3.91e-17 280.930
DEMetro_Z 10 63.979 9.07e-19 293.120
DEMetro_Z 12 69.711 2.81e-19 345.613
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 12.630 4.84e-09 3.261
DEMetro_Z_vs_SMC 1 7.410 3.3e-06 1.913
DEMetro_Z_vs_SMC 2 8.110 1.17e-06 2.094
DEMetro_Z_vs_SMC 3 7.670 2.23e-06 1.981
DEMetro_Z_vs_SMC 4 8.381 7.94e-07 2.164
DEMetro_Z_vs_SMC 5 11.564 1.5e-08 2.986
HMC_vs_Metro 0 -1.394 0.185 -0.360
HMC_vs_Metro 1 -2.115 0.0528 -0.546
HMC_vs_Metro 2 -2.342 0.0345 -0.605
HMC_vs_Metro 3 -9.316 2.23e-07 -2.405
HMC_vs_Metro 4 -3.938 0.00149 -1.017
HMC_vs_Metro 5 -1.462 0.166 -0.378
Metro_vs_DEMetro_Z 0 -26.054 2.91e-13 -6.727
Metro_vs_DEMetro_Z 1 -15.794 2.57e-10 -4.078
Metro_vs_DEMetro_Z 2 -15.545 3.17e-10 -4.014
Metro_vs_DEMetro_Z 3 -6.558 1.27e-05 -1.693
Metro_vs_DEMetro_Z 4 -13.815 1.5e-09 -3.567
Metro_vs_DEMetro_Z 5 -12.162 7.87e-09 -3.140
HMC_vs_SMC 0 -24.258 7.74e-13 -6.263
HMC_vs_SMC 1 -12.836 3.92e-09 -3.314
HMC_vs_SMC 2 -20.354 8.47e-12 -5.255
HMC_vs_SMC 3 -27.900 1.13e-13 -7.204
HMC_vs_SMC 4 -20.502 7.68e-12 -5.294
HMC_vs_SMC 5 -17.342 7.36e-11 -4.478
Metro_vs_SMC 0 -20.370 8.39e-12 -5.259
Metro_vs_SMC 1 -12.813 4.01e-09 -3.308
Metro_vs_SMC 2 -11.231 2.18e-08 -2.900
Metro_vs_SMC 3 -2.733 0.0162 -0.706
Metro_vs_SMC 4 -11.623 1.41e-08 -3.001
Metro_vs_SMC 5 -9.315 2.23e-07 -2.405
HMC_vs_DEMetro_Z 0 -28.113 1.02e-13 -7.259
HMC_vs_DEMetro_Z 1 -15.004 5.07e-10 -3.874
HMC_vs_DEMetro_Z 2 -25.846 3.25e-13 -6.673
HMC_vs_DEMetro_Z 3 -22.565 2.08e-12 -5.826
HMC_vs_DEMetro_Z 4 -23.774 1.02e-12 -6.138
HMC_vs_DEMetro_Z 5 -20.568 7.35e-12 -5.311
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.075 0.015 0.002 31.330
HMC 4 0.111 0.015 0.001 75.739
HMC 6 0.074 0.015 0.001 50.884
HMC 8 0.078 0.015 0.002 36.414
HMC 10 0.079 0.014 0.002 41.195
HMC 12 0.132 0.014 0.001 87.083
SMC 0 0.407 0.015 0.002 203.948
SMC 4 0.408 0.015 0.001 309.718
SMC 6 0.404 0.015 0.001 336.140
SMC 8 0.416 0.015 0.002 232.310
SMC 10 0.405 0.014 0.002 249.384
SMC 12 0.407 0.014 0.001 290.966
Metro 0 0.107 0.015 0.002 47.668
Metro 4 0.162 0.015 0.001 115.968
Metro 6 0.140 0.015 0.001 108.037
Metro 8 0.350 0.015 0.002 193.752
Metro 10 0.153 0.014 0.002 88.555
Metro 12 0.170 0.014 0.001 115.516
DEMetro_Z 0 0.489 0.015 0.002 246.507
DEMetro_Z 4 0.482 0.015 0.001 367.656
DEMetro_Z 6 0.483 0.015 0.001 403.902
DEMetro_Z 8 0.500 0.015 0.002 280.930
DEMetro_Z 10 0.473 0.014 0.002 293.120
DEMetro_Z 12 0.480 0.014 0.001 345.613
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.469 0.164 3.660
HMC 4 0.050 0.961 0.024
HMC 6 1.579 0.136 6.531
HMC 8 1.660 0.118 3.299
HMC 10 3.581 0.00288 7.352
HMC 12 2.487 0.0261 28.016
SMC 0 17.615 3.72e-11 37.321
SMC 4 26.678 1.88e-13 133.547
SMC 6 19.012 1.3e-11 40.403
SMC 8 28.598 5.93e-14 88.854
SMC 10 18.942 2.04e-11 91.824
SMC 12 23.718 1.01e-12 194.078
Metro 0 5.695 2.02e-05 4.022
Metro 4 5.665 5.29e-05 12.922
Metro 6 4.582 0.000292 4.258
Metro 8 1.501 0.156 19.950
Metro 10 4.514 0.000434 7.635
Metro 12 8.165 9.58e-07 22.696
DEMetro_Z 0 19.006 2.12e-11 251.144
DEMetro_Z 4 12.059 8.78e-09 617.849
DEMetro_Z 6 18.029 4.28e-11 187.797
DEMetro_Z 8 13.866 1.43e-09 392.124
DEMetro_Z 10 7.584 2.53e-06 513.219
DEMetro_Z 12 13.311 2.44e-09 966.743
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -18.815 2.46e-11 -4.858
HMC_vs_DEMetro_Z 1 -12.104 8.38e-09 -3.125
HMC_vs_DEMetro_Z 2 -17.833 5.06e-11 -4.604
HMC_vs_DEMetro_Z 3 -13.758 1.59e-09 -3.552
HMC_vs_DEMetro_Z 4 -7.452 3.1e-06 -1.924
HMC_vs_DEMetro_Z 5 -12.073 8.66e-09 -3.117
Metro_vs_SMC 0 -14.581 7.4e-10 -3.765
Metro_vs_SMC 1 -20.978 5.63e-12 -5.416
Metro_vs_SMC 2 -16.396 1.56e-10 -4.233
Metro_vs_SMC 3 -4.800 0.000283 -1.239
Metro_vs_SMC 4 -19.067 2.05e-11 -4.923
Metro_vs_SMC 5 -17.369 7.21e-11 -4.485
Metro_vs_DEMetro_Z 0 -18.905 2.3e-11 -4.881
Metro_vs_DEMetro_Z 1 -11.577 1.48e-08 -2.989
Metro_vs_DEMetro_Z 2 -17.872 4.91e-11 -4.615
Metro_vs_DEMetro_Z 3 -12.771 4.19e-09 -3.298
Metro_vs_DEMetro_Z 4 -7.436 3.17e-06 -1.920
Metro_vs_DEMetro_Z 5 -13.250 2.6e-09 -3.421
HMC_vs_Metro 0 -0.151 0.882 -0.039
HMC_vs_Metro 1 -5.721 5.28e-05 -1.477
HMC_vs_Metro 2 0.530 0.604 0.137
HMC_vs_Metro 3 -1.232 0.238 -0.318
HMC_vs_Metro 4 -0.156 0.878 -0.040
HMC_vs_Metro 5 0.437 0.669 0.113
HMC_vs_SMC 0 -17.372 7.19e-11 -4.485
HMC_vs_SMC 1 -26.600 2.19e-13 -6.868
HMC_vs_SMC 2 -7.149 4.94e-06 -1.846
HMC_vs_SMC 3 -26.769 2e-13 -6.912
HMC_vs_SMC 4 -17.005 9.58e-11 -4.391
HMC_vs_SMC 5 -11.169 2.34e-08 -2.884
DEMetro_Z_vs_SMC 0 16.787 1.14e-10 4.335
DEMetro_Z_vs_SMC 1 9.737 1.3e-07 2.514
DEMetro_Z_vs_SMC 2 14.439 8.42e-10 3.728
DEMetro_Z_vs_SMC 3 10.949 3.01e-08 2.827
DEMetro_Z_vs_SMC 4 6.019 3.15e-05 1.554
DEMetro_Z_vs_SMC 5 10.622 4.4e-08 2.743
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.135 0.071 0.017 3.660
HMC 4 0.062 0.062 0.009 0.024
HMC 6 0.234 0.067 0.026 6.531
HMC 8 0.257 0.084 0.052 3.299
HMC 10 0.152 0.070 0.011 7.352
HMC 12 0.317 0.066 0.009 28.016
SMC 0 0.723 0.071 0.017 37.321
SMC 4 1.261 0.062 0.009 133.547
SMC 6 1.104 0.067 0.026 40.403
SMC 8 4.745 0.084 0.052 88.854
SMC 10 1.102 0.070 0.011 91.824
SMC 12 1.802 0.066 0.009 194.078
Metro 0 0.142 0.071 0.017 4.022
Metro 4 0.178 0.062 0.009 12.922
Metro 6 0.176 0.067 0.026 4.258
Metro 8 1.131 0.084 0.052 19.950
Metro 10 0.155 0.070 0.011 7.635
Metro 12 0.269 0.066 0.009 22.696
DEMetro_Z 0 4.456 0.071 0.017 251.144
DEMetro_Z 4 5.609 0.062 0.009 617.849
DEMetro_Z 6 4.889 0.067 0.026 187.797
DEMetro_Z 8 20.654 0.084 0.052 392.124
DEMetro_Z 10 5.840 0.070 0.011 513.219
DEMetro_Z 12 8.716 0.066 0.009 966.743
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.279 0.221 3.945
HMC 4 1.533 0.141 0.940
HMC 6 0.973 0.345 1.001
HMC 8 -1.224 0.241 -0.317
HMC 10 0.119 0.907 0.053
HMC 12 0.362 0.721 0.177
SMC 0 183.504 1.43e-30 136.513
SMC 4 147.151 6.88e-24 602.467
SMC 6 202.304 1.64e-29 180.315
SMC 8 43.386 6.98e-17 74.538
SMC 10 149.953 1e-24 261.274
SMC 12 59.970 1.51e-18 160.414
Metro 0 0.566 0.579 0.468
Metro 4 2.534 0.0219 2.378
Metro 6 1.141 0.264 0.406
Metro 8 1.016 0.327 26.648
Metro 10 -0.284 0.779 -0.094
Metro 12 1.272 0.216 0.634
DEMetro_Z 0 6.602 1.06e-05 15.860
DEMetro_Z 4 5.539 7.27e-05 63.990
DEMetro_Z 6 7.529 2.41e-06 18.565
DEMetro_Z 8 8.756 4.2e-07 25.947
DEMetro_Z 10 4.175 0.000932 33.899
DEMetro_Z 12 7.274 3.81e-06 24.930
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -39.798 8.33e-16 -10.276
HMC_vs_SMC 1 -134.834 3.35e-23 -34.814
HMC_vs_SMC 2 -127.463 7.35e-23 -32.911
HMC_vs_SMC 3 -44.053 2.03e-16 -11.374
HMC_vs_SMC 4 -150.687 7.07e-24 -38.907
HMC_vs_SMC 5 -59.929 2.79e-18 -15.474
Metro_vs_DEMetro_Z 0 -5.984 3.34e-05 -1.545
Metro_vs_DEMetro_Z 1 -5.308 0.00011 -1.371
Metro_vs_DEMetro_Z 2 -7.507 2.85e-06 -1.938
Metro_vs_DEMetro_Z 3 0.027 0.979 0.007
Metro_vs_DEMetro_Z 4 -4.151 0.00098 -1.072
Metro_vs_DEMetro_Z 5 -7.457 3.08e-06 -1.925
HMC_vs_Metro 0 1.252 0.231 0.323
HMC_vs_Metro 1 -2.246 0.0414 -0.580
HMC_vs_Metro 2 0.566 0.58 0.146
HMC_vs_Metro 3 -1.028 0.321 -0.265
HMC_vs_Metro 4 0.430 0.674 0.111
HMC_vs_Metro 5 -2.471 0.0269 -0.638
HMC_vs_DEMetro_Z 0 -3.527 0.00335 -0.911
HMC_vs_DEMetro_Z 1 -5.400 9.35e-05 -1.394
HMC_vs_DEMetro_Z 2 -6.157 2.49e-05 -1.590
HMC_vs_DEMetro_Z 3 -8.911 3.82e-07 -2.301
HMC_vs_DEMetro_Z 4 -4.110 0.00106 -1.061
HMC_vs_DEMetro_Z 5 -7.553 2.66e-06 -1.950
Metro_vs_SMC 0 -102.648 1.52e-21 -26.504
Metro_vs_SMC 1 -125.103 9.54e-23 -32.301
Metro_vs_SMC 2 -182.931 4.69e-25 -47.233
Metro_vs_SMC 3 -1.787 0.0957 -0.461
Metro_vs_SMC 4 -150.752 7.02e-24 -38.924
Metro_vs_SMC 5 -59.627 3e-18 -15.396
DEMetro_Z_vs_SMC 0 -50.529 3.01e-17 -13.047
DEMetro_Z_vs_SMC 1 -44.514 1.76e-16 -11.493
DEMetro_Z_vs_SMC 2 -69.452 3.57e-19 -17.932
DEMetro_Z_vs_SMC 3 -12.702 4.5e-09 -3.280
DEMetro_Z_vs_SMC 4 -27.792 1.2e-13 -7.176
DEMetro_Z_vs_SMC 5 -31.756 1.9e-14 -8.199
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 46.845 11.222 9.030 3.945
HMC 4 6.636 3.824 2.992 0.940
HMC 6 15.836 6.080 9.746 1.001
HMC 8 7.006 40.803 106.713 -0.317
HMC 10 7.358 7.004 6.719 0.053
HMC 12 13.018 9.345 20.708 0.177
SMC 0 1243.867 11.222 9.030 136.513
SMC 4 1806.509 3.824 2.992 602.467
SMC 6 1763.350 6.080 9.746 180.315
SMC 8 7995.002 40.803 106.713 74.538
SMC 10 1762.589 7.004 6.719 261.274
SMC 12 3331.259 9.345 20.708 160.414
Metro 0 15.446 11.222 9.030 0.468
Metro 4 10.939 3.824 2.992 2.378
Metro 6 10.037 6.080 9.746 0.406
Metro 8 2884.525 40.803 106.713 26.648
Metro 10 6.374 7.004 6.719 -0.094
Metro 12 22.466 9.345 20.708 0.634
DEMetro_Z 0 154.433 11.222 9.030 15.860
DEMetro_Z 4 195.292 3.824 2.992 63.990
DEMetro_Z 6 187.009 6.080 9.746 18.565
DEMetro_Z 8 2809.658 40.803 106.713 25.947
DEMetro_Z 10 234.781 7.004 6.719 33.899
DEMetro_Z 12 525.597 9.345 20.708 24.930
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.449 0.169 62.826
HMC 4 2.979 0.00988 11.797
HMC 6 1.544 0.145 28.720
HMC 8 2.081 0.056 5.620
HMC 10 3.591 0.0029 11.490
HMC 12 2.260 0.0402 13.758
SMC 0 485.852 1.85e-31 1351.416
SMC 4 282.962 9.72e-28 2821.172
SMC 6 404.928 3.23e-30 1304.093
SMC 8 90.239 8.95e-21 1242.138
SMC 10 287.790 6.94e-28 1862.401
SMC 12 112.564 4.12e-22 2195.324
Metro 0 5.647 5.57e-05 14.215
Metro 4 3.102 0.0078 47.732
Metro 6 3.667 0.00253 21.879
Metro 8 1.516 0.152 106.596
Metro 10 7.831 1.4e-06 15.366
Metro 12 4.190 0.000906 41.207
DEMetro_Z 0 13.235 2.63e-09 425.158
DEMetro_Z 4 10.668 4.17e-08 839.871
DEMetro_Z 6 15.975 2.2e-10 379.798
DEMetro_Z 8 19.636 1.38e-11 691.882
DEMetro_Z 10 9.498 1.76e-07 590.162
DEMetro_Z 12 12.310 6.74e-09 825.779
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -12.814 4.01e-09 -3.308
Metro_vs_DEMetro_Z 1 -9.257 2.41e-07 -2.390
Metro_vs_DEMetro_Z 2 -14.970 5.23e-10 -3.865
Metro_vs_DEMetro_Z 3 -7.914 1.55e-06 -2.043
Metro_vs_DEMetro_Z 4 -9.334 2.18e-07 -2.410
Metro_vs_DEMetro_Z 5 -11.798 1.16e-08 -3.046
DEMetro_Z_vs_SMC 0 -29.240 5.94e-14 -7.550
DEMetro_Z_vs_SMC 1 -25.374 4.18e-13 -6.552
DEMetro_Z_vs_SMC 2 -39.631 8.83e-16 -10.233
DEMetro_Z_vs_SMC 3 -14.070 1.18e-09 -3.633
DEMetro_Z_vs_SMC 4 -20.478 7.81e-12 -5.287
DEMetro_Z_vs_SMC 5 -20.455 7.92e-12 -5.282
HMC_vs_DEMetro_Z 0 -8.017 1.34e-06 -2.070
HMC_vs_DEMetro_Z 1 -10.385 5.84e-08 -2.681
HMC_vs_DEMetro_Z 2 -11.308 2e-08 -2.920
HMC_vs_DEMetro_Z 3 -20.121 9.91e-12 -5.195
HMC_vs_DEMetro_Z 4 -9.148 2.78e-07 -2.362
HMC_vs_DEMetro_Z 5 -11.706 1.28e-08 -3.023
HMC_vs_Metro 0 1.110 0.286 0.287
HMC_vs_Metro 1 -2.837 0.0132 -0.733
HMC_vs_Metro 2 0.367 0.719 0.095
HMC_vs_Metro 3 -1.433 0.174 -0.370
HMC_vs_Metro 4 -0.979 0.344 -0.253
HMC_vs_Metro 5 -2.117 0.0527 -0.547
HMC_vs_SMC 0 -29.786 4.61e-14 -7.691
HMC_vs_SMC 1 -208.983 7.27e-26 -53.959
HMC_vs_SMC 2 -66.934 5.97e-19 -17.282
HMC_vs_SMC 3 -89.587 1.02e-20 -23.131
HMC_vs_SMC 4 -281.246 1.14e-27 -72.617
HMC_vs_SMC 5 -99.467 2.36e-21 -25.682
Metro_vs_SMC 0 -390.339 1.16e-29 -100.785
Metro_vs_SMC 1 -114.622 3.25e-22 -29.595
Metro_vs_SMC 2 -170.511 1.25e-24 -44.026
Metro_vs_SMC 3 -14.983 5.17e-10 -3.869
Metro_vs_SMC 4 -333.880 1.03e-28 -86.207
Metro_vs_SMC 5 -100.316 2.09e-21 -25.901
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 1.365 0.124 0.020 62.826
HMC 4 0.245 0.110 0.011 11.797
HMC 6 0.817 0.115 0.024 28.720
HMC 8 0.445 0.137 0.055 5.620
HMC 10 0.318 0.122 0.017 11.490
HMC 12 0.396 0.121 0.020 13.758
SMC 0 26.831 0.124 0.020 1351.416
SMC 4 32.460 0.110 0.011 2821.172
SMC 6 31.980 0.115 0.024 1304.093
SMC 8 68.202 0.137 0.055 1242.138
SMC 10 31.874 0.122 0.017 1862.401
SMC 12 43.975 0.121 0.020 2195.324
Metro 0 0.405 0.124 0.020 14.215
Metro 4 0.657 0.110 0.011 47.732
Metro 6 0.650 0.115 0.024 21.879
Metro 8 5.978 0.137 0.055 106.596
Metro 10 0.384 0.122 0.017 15.366
Metro 12 0.944 0.121 0.020 41.207
DEMetro_Z 0 8.526 0.124 0.020 425.158
DEMetro_Z 4 9.741 0.110 0.011 839.871
DEMetro_Z 6 9.396 0.115 0.024 379.798
DEMetro_Z 8 38.050 0.137 0.055 691.882
DEMetro_Z 10 10.184 0.122 0.017 590.162
DEMetro_Z 12 16.617 0.121 0.020 825.779
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.195 0.0455 46.412
HMC 4 3.970 0.00138 19.969
HMC 6 2.051 0.0595 87.809
HMC 8 2.014 0.0636 60.739
HMC 10 5.048 0.000176 28.045
HMC 12 2.190 0.0459 71.951
SMC 0 132.500 3.58e-24 204.801
SMC 4 130.807 1.81e-23 309.927
SMC 6 135.945 1.2e-23 345.957
SMC 8 138.595 2.67e-24 231.717
SMC 10 111.739 1.61e-22 255.352
SMC 12 193.113 1.31e-26 296.381
Metro 0 6.576 1.21e-05 35.031
Metro 4 4.583 0.000425 76.974
Metro 6 4.866 0.000249 85.387
Metro 8 5.038 0.000181 121.042
Metro 10 6.257 2.07e-05 37.453
Metro 12 6.052 2.97e-05 88.353
DEMetro_Z 0 27.393 1.41e-13 260.065
DEMetro_Z 4 23.384 1.27e-12 427.860
DEMetro_Z 6 36.731 2.47e-15 422.480
DEMetro_Z 8 31.961 1.69e-14 321.141
DEMetro_Z 10 28.004 1.05e-13 324.634
DEMetro_Z 12 42.119 3.63e-16 391.504
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.725 5.25e-05 1.478
DEMetro_Z_vs_SMC 1 6.358 1.77e-05 1.642
DEMetro_Z_vs_SMC 2 5.896 3.9e-05 1.522
DEMetro_Z_vs_SMC 3 8.757 4.71e-07 2.261
DEMetro_Z_vs_SMC 4 5.492 7.94e-05 1.418
DEMetro_Z_vs_SMC 5 10.471 5.27e-08 2.704
HMC_vs_Metro 0 0.499 0.625 0.129
HMC_vs_Metro 1 -3.659 0.00258 -0.945
HMC_vs_Metro 2 0.052 0.96 0.013
HMC_vs_Metro 3 -1.803 0.093 -0.465
HMC_vs_Metro 4 -1.236 0.237 -0.319
HMC_vs_Metro 5 -0.410 0.688 -0.106
Metro_vs_DEMetro_Z 0 -20.915 5.86e-12 -5.400
Metro_vs_DEMetro_Z 1 -12.717 4.42e-09 -3.284
Metro_vs_DEMetro_Z 2 -16.719 1.2e-10 -4.317
Metro_vs_DEMetro_Z 3 -7.788 1.87e-06 -2.011
Metro_vs_DEMetro_Z 4 -20.523 7.57e-12 -5.299
Metro_vs_DEMetro_Z 5 -18.869 2.36e-11 -4.872
HMC_vs_SMC 0 -7.690 2.16e-06 -1.985
HMC_vs_SMC 1 -51.968 2.04e-17 -13.418
HMC_vs_SMC 2 -6.142 2.55e-05 -1.586
HMC_vs_SMC 3 -5.755 4.98e-05 -1.486
HMC_vs_SMC 4 -35.172 4.63e-15 -9.081
HMC_vs_SMC 5 -6.669 1.06e-05 -1.722
Metro_vs_SMC 0 -31.798 1.87e-14 -8.210
Metro_vs_SMC 1 -12.915 3.62e-09 -3.335
Metro_vs_SMC 2 -15.114 4.6e-10 -3.902
Metro_vs_SMC 3 -4.605 0.000408 -1.189
Metro_vs_SMC 4 -32.757 1.24e-14 -8.458
Metro_vs_SMC 5 -15.182 4.34e-10 -3.920
HMC_vs_DEMetro_Z 0 -9.081 3.04e-07 -2.345
HMC_vs_DEMetro_Z 1 -22.136 2.71e-12 -5.716
HMC_vs_DEMetro_Z 2 -7.273 4.08e-06 -1.878
HMC_vs_DEMetro_Z 3 -7.928 1.52e-06 -2.047
HMC_vs_DEMetro_Z 4 -21.783 3.37e-12 -5.624
HMC_vs_DEMetro_Z 5 -8.790 4.5e-07 -2.270
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.104 0.015 0.002 46.412
HMC 4 0.040 0.015 0.001 19.969
HMC 6 0.116 0.015 0.001 87.809
HMC 8 0.120 0.015 0.002 60.739
HMC 10 0.058 0.014 0.002 28.045
HMC 12 0.111 0.014 0.001 71.951
SMC 0 0.409 0.015 0.002 204.801
SMC 4 0.408 0.015 0.001 309.927
SMC 6 0.416 0.015 0.001 345.957
SMC 8 0.415 0.015 0.002 231.717
SMC 10 0.414 0.014 0.002 255.352
SMC 12 0.414 0.014 0.001 296.381
Metro 0 0.082 0.015 0.002 35.031
Metro 4 0.112 0.015 0.001 76.974
Metro 6 0.114 0.015 0.001 85.387
Metro 8 0.224 0.015 0.002 121.042
Metro 10 0.073 0.014 0.002 37.453
Metro 12 0.133 0.014 0.001 88.353
DEMetro_Z 0 0.515 0.015 0.002 260.065
DEMetro_Z 4 0.558 0.015 0.001 427.860
DEMetro_Z 6 0.504 0.015 0.001 422.480
DEMetro_Z 8 0.570 0.015 0.002 321.141
DEMetro_Z 10 0.523 0.014 0.002 324.634
DEMetro_Z 12 0.542 0.014 0.001 391.504
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

Varying_Mode_Distance_with_Corr_and_Tails (Mixture, mm, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 2.866 0.00952 1.712
HMC 4 3.535 0.00169 1.674
HMC 6 1.226 0.231 0.390
HMC 8 0.765 0.451 0.246
HMC 10 2.664 0.0129 1.096
HMC 12 3.641 0.00213 3.337
SMC 0 3.457 0.00253 2.126
SMC 4 2.134 0.0467 1.523
SMC 6 1.017 0.32 0.296
SMC 8 2.736 0.0113 1.250
SMC 10 1.788 0.085 0.729
SMC 12 4.041 0.000622 2.379
Metro 0 4.282 0.000667 6.323
Metro 4 4.428 0.000507 7.011
Metro 6 1.770 0.0876 0.626
Metro 8 2.390 0.0246 1.065
Metro 10 2.494 0.0225 1.770
Metro 12 5.068 0.000101 4.403
DEMetro_Z 0 2.624 0.0191 3.414
DEMetro_Z 4 2.173 0.047 4.950
DEMetro_Z 6 0.983 0.338 0.671
DEMetro_Z 8 3.145 0.00519 1.959
DEMetro_Z 10 3.482 0.00261 2.436
DEMetro_Z 12 4.638 0.000274 4.652
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.180 0.258 -0.305
HMC_vs_DEMetro_Z 1 -1.363 0.194 -0.352
HMC_vs_DEMetro_Z 2 -0.468 0.647 -0.121
HMC_vs_DEMetro_Z 3 -3.081 0.00814 -0.795
HMC_vs_DEMetro_Z 4 -1.787 0.0955 -0.462
HMC_vs_DEMetro_Z 5 -1.104 0.288 -0.285
Metro_vs_SMC 0 2.546 0.0233 0.657
Metro_vs_SMC 1 2.822 0.0136 0.729
Metro_vs_SMC 2 1.348 0.199 0.348
Metro_vs_SMC 3 -0.356 0.727 -0.092
Metro_vs_SMC 4 1.346 0.2 0.347
Metro_vs_SMC 5 2.550 0.0231 0.658
Metro_vs_DEMetro_Z 0 1.308 0.212 0.338
Metro_vs_DEMetro_Z 1 0.758 0.461 0.196
Metro_vs_DEMetro_Z 2 -0.065 0.949 -0.017
Metro_vs_DEMetro_Z 3 -1.404 0.182 -0.362
Metro_vs_DEMetro_Z 4 -0.739 0.472 -0.191
Metro_vs_DEMetro_Z 5 -0.201 0.843 -0.052
HMC_vs_Metro 0 -3.339 0.00487 -0.862
HMC_vs_Metro 1 -3.430 0.00407 -0.885
HMC_vs_Metro 2 -0.695 0.498 -0.179
HMC_vs_Metro 3 -2.729 0.0163 -0.705
HMC_vs_Metro 4 -0.827 0.422 -0.214
HMC_vs_Metro 5 -0.843 0.413 -0.218
HMC_vs_SMC 0 -0.503 0.623 -0.130
HMC_vs_SMC 1 0.163 0.873 0.042
HMC_vs_SMC 2 0.504 0.622 0.130
HMC_vs_SMC 3 -2.292 0.0379 -0.592
HMC_vs_SMC 4 0.758 0.461 0.196
HMC_vs_SMC 5 0.873 0.397 0.225
DEMetro_Z_vs_SMC 0 1.088 0.295 0.281
DEMetro_Z_vs_SMC 1 1.378 0.19 0.356
DEMetro_Z_vs_SMC 2 0.600 0.558 0.155
DEMetro_Z_vs_SMC 3 1.080 0.298 0.279
DEMetro_Z_vs_SMC 4 3.310 0.00516 0.855
DEMetro_Z_vs_SMC 5 2.065 0.0579 0.533
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.121 0.053 0.040 1.712
HMC 4 0.110 0.054 0.033 1.674
HMC 6 0.126 0.083 0.111 0.390
HMC 8 0.132 0.091 0.165 0.246
HMC 10 0.143 0.069 0.067 1.096
HMC 12 0.170 0.053 0.035 3.337
SMC 0 0.138 0.053 0.040 2.126
SMC 4 0.105 0.054 0.033 1.523
SMC 6 0.115 0.083 0.111 0.296
SMC 8 0.298 0.091 0.165 1.250
SMC 10 0.119 0.069 0.067 0.729
SMC 12 0.136 0.053 0.035 2.379
Metro 0 0.304 0.053 0.040 6.323
Metro 4 0.287 0.054 0.033 7.011
Metro 6 0.152 0.083 0.111 0.626
Metro 8 0.267 0.091 0.165 1.065
Metro 10 0.189 0.069 0.067 1.770
Metro 12 0.208 0.053 0.035 4.403
DEMetro_Z 0 0.189 0.053 0.040 3.414
DEMetro_Z 4 0.218 0.054 0.033 4.950
DEMetro_Z 6 0.157 0.083 0.111 0.671
DEMetro_Z 8 0.415 0.091 0.165 1.959
DEMetro_Z 10 0.234 0.069 0.067 2.436
DEMetro_Z 12 0.216 0.053 0.035 4.652
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 -1.050 0.311 -0.272
HMC 4 1.845 0.0767 0.811
HMC 6 -0.929 0.368 -0.241
HMC 8 -0.578 0.571 -0.160
HMC 10 -1.117 0.282 -0.291
HMC 12 -0.094 0.926 -0.032
SMC 0 -0.598 0.559 -0.156
SMC 4 5.445 6.66e-05 7.336
SMC 6 -0.877 0.395 -0.227
SMC 8 0.125 0.902 0.034
SMC 10 -0.346 0.734 -0.092
SMC 12 0.832 0.413 0.262
Metro 0 -0.997 0.335 -0.258
Metro 4 0.970 0.342 0.454
Metro 6 -1.067 0.304 -0.276
Metro 8 -0.561 0.582 -0.155
Metro 10 -0.787 0.443 -0.210
Metro 12 0.385 0.703 0.155
DEMetro_Z 0 -0.493 0.628 -0.132
DEMetro_Z 4 1.926 0.0731 2.534
DEMetro_Z 6 -1.056 0.309 -0.273
DEMetro_Z 8 -0.530 0.603 -0.146
DEMetro_Z 10 -1.072 0.301 -0.279
DEMetro_Z 12 0.317 0.754 0.125
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.916 0.0113 -0.753
HMC_vs_SMC 1 -5.026 0.000185 -1.298
HMC_vs_SMC 2 -0.475 0.642 -0.123
HMC_vs_SMC 3 -4.619 0.000398 -1.193
HMC_vs_SMC 4 -2.438 0.0287 -0.630
HMC_vs_SMC 5 -1.223 0.241 -0.316
Metro_vs_DEMetro_Z 0 -1.842 0.0867 -0.476
Metro_vs_DEMetro_Z 1 -1.585 0.135 -0.409
Metro_vs_DEMetro_Z 2 -1.129 0.278 -0.291
Metro_vs_DEMetro_Z 3 -0.916 0.375 -0.237
Metro_vs_DEMetro_Z 4 0.997 0.336 0.257
Metro_vs_DEMetro_Z 5 0.317 0.756 0.082
HMC_vs_Metro 0 -0.586 0.567 -0.151
HMC_vs_Metro 1 0.783 0.446 0.202
HMC_vs_Metro 2 1.094 0.293 0.282
HMC_vs_Metro 3 -2.975 0.01 -0.768
HMC_vs_Metro 4 -1.034 0.319 -0.267
HMC_vs_Metro 5 -0.763 0.458 -0.197
HMC_vs_DEMetro_Z 0 -2.409 0.0303 -0.622
HMC_vs_DEMetro_Z 1 -1.308 0.212 -0.338
HMC_vs_DEMetro_Z 2 1.045 0.314 0.270
HMC_vs_DEMetro_Z 3 -1.313 0.21 -0.339
HMC_vs_DEMetro_Z 4 -0.313 0.759 -0.081
HMC_vs_DEMetro_Z 5 -0.749 0.466 -0.193
Metro_vs_SMC 0 -2.017 0.0633 -0.521
Metro_vs_SMC 1 -4.849 0.000258 -1.252
Metro_vs_SMC 2 -3.999 0.00132 -1.032
Metro_vs_SMC 3 -4.498 0.000502 -1.161
Metro_vs_SMC 4 -1.460 0.166 -0.377
Metro_vs_SMC 5 -0.431 0.673 -0.111
DEMetro_Z_vs_SMC 0 0.332 0.745 0.086
DEMetro_Z_vs_SMC 1 -2.555 0.0229 -0.660
DEMetro_Z_vs_SMC 2 -3.925 0.00153 -1.013
DEMetro_Z_vs_SMC 3 -4.437 0.000564 -1.146
DEMetro_Z_vs_SMC 4 -2.231 0.0425 -0.576
DEMetro_Z_vs_SMC 5 -0.523 0.609 -0.135
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 3.971 16.297 45.265 -0.272
HMC 4 3.561 2.133 1.761 0.811
HMC 6 9.356 52.717 179.621 -0.241
HMC 8 42.472 105.394 394.325 -0.160
HMC 10 4.053 11.724 26.319 -0.291
HMC 12 4.071 4.249 5.608 -0.032
SMC 0 9.235 16.297 45.265 -0.156
SMC 4 15.049 2.133 1.761 7.336
SMC 6 12.024 52.717 179.621 -0.227
SMC 8 118.862 105.394 394.325 0.034
SMC 10 9.308 11.724 26.319 -0.092
SMC 12 5.721 4.249 5.608 0.262
Metro 0 4.603 16.297 45.265 -0.258
Metro 4 2.931 2.133 1.761 0.454
Metro 6 3.216 52.717 179.621 -0.276
Metro 8 44.308 105.394 394.325 -0.155
Metro 10 6.189 11.724 26.319 -0.210
Metro 12 5.121 4.249 5.608 0.155
DEMetro_Z 0 10.323 16.297 45.265 -0.132
DEMetro_Z 4 6.594 2.133 1.761 2.534
DEMetro_Z 6 3.728 52.717 179.621 -0.273
DEMetro_Z 8 47.755 105.394 394.325 -0.146
DEMetro_Z 10 4.377 11.724 26.319 -0.279
DEMetro_Z 12 4.949 4.249 5.608 0.125
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.145 0.000332 1.831
HMC 4 6.188 6.81e-06 4.248
HMC 6 1.942 0.0624 0.760
HMC 8 1.926 0.0649 0.632
HMC 10 5.792 7.68e-06 3.028
HMC 12 5.798 3.04e-05 6.500
SMC 0 7.408 2.48e-06 12.287
SMC 4 7.972 1.35e-06 31.810
SMC 6 5.867 1.59e-05 4.404
SMC 8 7.567 2.18e-06 16.368
SMC 10 8.475 3.48e-07 10.047
SMC 12 7.833 1.26e-06 12.757
Metro 0 6.594 5.83e-06 6.313
Metro 4 8.146 7.13e-07 11.763
Metro 6 4.445 0.000126 1.632
Metro 8 4.682 8.41e-05 2.102
Metro 10 3.387 0.00411 5.038
Metro 12 8.502 2.75e-07 8.933
DEMetro_Z 0 3.513 0.0032 5.470
DEMetro_Z 4 3.546 0.00317 11.389
DEMetro_Z 6 3.206 0.00427 1.819
DEMetro_Z 8 4.293 0.000522 3.836
DEMetro_Z 10 5.898 1.68e-05 4.750
DEMetro_Z 12 7.958 7.44e-07 9.164
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.414 0.685 0.107
Metro_vs_DEMetro_Z 1 0.115 0.91 0.030
Metro_vs_DEMetro_Z 2 -0.320 0.753 -0.083
Metro_vs_DEMetro_Z 3 -2.520 0.0245 -0.651
Metro_vs_DEMetro_Z 4 0.172 0.866 0.045
Metro_vs_DEMetro_Z 5 -0.217 0.831 -0.056
DEMetro_Z_vs_SMC 0 -3.244 0.00588 -0.838
DEMetro_Z_vs_SMC 1 -4.186 0.000914 -1.081
DEMetro_Z_vs_SMC 2 -2.940 0.0107 -0.759
DEMetro_Z_vs_SMC 3 -5.823 4.42e-05 -1.503
DEMetro_Z_vs_SMC 4 -4.453 0.000546 -1.150
DEMetro_Z_vs_SMC 5 -1.985 0.0671 -0.513
HMC_vs_DEMetro_Z 0 -2.343 0.0344 -0.605
HMC_vs_DEMetro_Z 1 -2.004 0.0648 -0.517
HMC_vs_DEMetro_Z 2 -3.625 0.00276 -0.936
HMC_vs_DEMetro_Z 3 -3.696 0.0024 -0.954
HMC_vs_DEMetro_Z 4 -2.110 0.0534 -0.545
HMC_vs_DEMetro_Z 5 -2.171 0.0476 -0.561
HMC_vs_Metro 0 -4.452 0.000548 -1.149
HMC_vs_Metro 1 -4.366 0.000645 -1.127
HMC_vs_Metro 2 -1.970 0.0689 -0.509
HMC_vs_Metro 3 -4.371 0.00064 -1.129
HMC_vs_Metro 4 -1.180 0.258 -0.305
HMC_vs_Metro 5 -1.523 0.15 -0.393
HMC_vs_SMC 0 -6.541 1.31e-05 -1.689
HMC_vs_SMC 1 -7.232 4.34e-06 -1.867
HMC_vs_SMC 2 -4.517 0.000483 -1.166
HMC_vs_SMC 3 -7.272 4.08e-06 -1.878
HMC_vs_SMC 4 -6.224 2.22e-05 -1.607
HMC_vs_SMC 5 -4.135 0.00101 -1.068
Metro_vs_SMC 0 -2.712 0.0169 -0.700
Metro_vs_SMC 1 -4.361 0.000652 -1.126
Metro_vs_SMC 2 -4.619 0.000398 -1.193
Metro_vs_SMC 3 -6.636 1.12e-05 -1.713
Metro_vs_SMC 4 -3.033 0.00895 -0.783
Metro_vs_SMC 5 -1.815 0.091 -0.469
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.205 0.115 0.049 1.831
HMC 4 0.200 0.107 0.022 4.248
HMC 6 0.209 0.134 0.099 0.760
HMC 8 0.226 0.144 0.130 0.632
HMC 10 0.252 0.123 0.043 3.028
HMC 12 0.265 0.107 0.024 6.500
SMC 0 0.717 0.115 0.049 12.287
SMC 4 0.799 0.107 0.022 31.810
SMC 6 0.570 0.134 0.099 4.404
SMC 8 2.280 0.144 0.130 16.368
SMC 10 0.551 0.123 0.043 10.047
SMC 12 0.417 0.107 0.024 12.757
Metro 0 0.424 0.115 0.049 6.313
Metro 4 0.363 0.107 0.022 11.763
Metro 6 0.296 0.134 0.099 1.632
Metro 8 0.418 0.144 0.130 2.102
Metro 10 0.337 0.123 0.043 5.038
Metro 12 0.324 0.107 0.024 8.933
DEMetro_Z 0 0.383 0.115 0.049 5.470
DEMetro_Z 4 0.355 0.107 0.022 11.389
DEMetro_Z 6 0.314 0.134 0.099 1.819
DEMetro_Z 8 0.644 0.144 0.130 3.836
DEMetro_Z 10 0.325 0.123 0.043 4.750
DEMetro_Z 12 0.330 0.107 0.024 9.164
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 3.936 0.000661 1.973
HMC 4 5.001 9.88e-05 3.798
HMC 6 4.184 0.000534 2.895
HMC 8 4.572 0.000378 7.001
HMC 10 6.626 7.33e-06 8.136
HMC 12 6.441 1.35e-05 13.826
SMC 0 11.224 1.51e-08 21.537
SMC 4 11.008 2.33e-08 29.480
SMC 6 9.279 1.82e-07 19.342
SMC 8 11.190 2.22e-08 76.056
SMC 10 11.151 1.5e-08 19.221
SMC 12 9.263 1.89e-07 19.904
Metro 0 6.977 4.89e-06 11.217
Metro 4 7.545 1.87e-06 11.372
Metro 6 8.413 2.97e-07 8.545
Metro 8 6.767 8.24e-06 18.266
Metro 10 4.544 0.000416 8.278
Metro 12 7.745 1.53e-06 13.881
DEMetro_Z 0 4.765 0.000218 5.000
DEMetro_Z 4 7.841 6.36e-07 7.329
DEMetro_Z 6 6.243 1.58e-05 8.720
DEMetro_Z 8 7.605 2.26e-06 23.696
DEMetro_Z 10 5.079 0.000158 13.286
DEMetro_Z 12 5.921 3.52e-05 18.461
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -8.221 9.96e-07 -2.123
DEMetro_Z_vs_SMC 1 -7.556 2.65e-06 -1.951
DEMetro_Z_vs_SMC 2 -3.692 0.00242 -0.953
DEMetro_Z_vs_SMC 3 -6.766 9.08e-06 -1.747
DEMetro_Z_vs_SMC 4 -2.500 0.0255 -0.646
DEMetro_Z_vs_SMC 5 -0.447 0.661 -0.116
HMC_vs_Metro 0 -5.396 9.43e-05 -1.393
HMC_vs_Metro 1 -4.094 0.0011 -1.057
HMC_vs_Metro 2 -4.785 0.00029 -1.236
HMC_vs_Metro 3 -3.502 0.00352 -0.904
HMC_vs_Metro 4 -0.057 0.956 -0.015
HMC_vs_Metro 5 -0.017 0.986 -0.004
Metro_vs_DEMetro_Z 0 3.169 0.00683 0.818
Metro_vs_DEMetro_Z 1 2.733 0.0162 0.706
Metro_vs_DEMetro_Z 2 -0.108 0.915 -0.028
Metro_vs_DEMetro_Z 3 -1.496 0.157 -0.386
Metro_vs_DEMetro_Z 4 -1.475 0.162 -0.381
Metro_vs_DEMetro_Z 5 -1.181 0.257 -0.305
HMC_vs_SMC 0 -9.377 2.06e-07 -2.421
HMC_vs_SMC 1 -9.623 1.5e-07 -2.485
HMC_vs_SMC 2 -6.952 6.74e-06 -1.795
HMC_vs_SMC 3 -10.432 5.52e-08 -2.694
HMC_vs_SMC 4 -6.284 2.01e-05 -1.622
HMC_vs_SMC 5 -2.000 0.0653 -0.516
Metro_vs_SMC 0 -3.378 0.0045 -0.872
Metro_vs_SMC 1 -5.092 0.000164 -1.315
Metro_vs_SMC 2 -6.224 2.22e-05 -1.607
Metro_vs_SMC 3 -9.303 2.27e-07 -2.402
Metro_vs_SMC 4 -4.371 0.000639 -1.129
Metro_vs_SMC 5 -1.839 0.0872 -0.475
HMC_vs_DEMetro_Z 0 -2.573 0.0221 -0.664
HMC_vs_DEMetro_Z 1 -2.870 0.0124 -0.741
HMC_vs_DEMetro_Z 2 -4.184 0.000918 -1.080
HMC_vs_DEMetro_Z 3 -4.810 0.000277 -1.242
HMC_vs_DEMetro_Z 4 -2.120 0.0523 -0.547
HMC_vs_DEMetro_Z 5 -1.617 0.128 -0.417
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.028 0.015 0.006 1.973
HMC 4 0.032 0.016 0.004 3.798
HMC 6 0.028 0.014 0.005 2.895
HMC 8 0.036 0.013 0.003 7.001
HMC 10 0.048 0.014 0.004 8.136
HMC 12 0.051 0.012 0.003 13.826
SMC 0 0.151 0.015 0.006 21.537
SMC 4 0.144 0.016 0.004 29.480
SMC 6 0.109 0.014 0.005 19.342
SMC 8 0.263 0.013 0.003 76.056
SMC 10 0.094 0.014 0.004 19.221
SMC 12 0.068 0.012 0.003 19.904
Metro 0 0.086 0.015 0.006 11.217
Metro 4 0.065 0.016 0.004 11.372
Metro 6 0.056 0.014 0.005 8.545
Metro 8 0.073 0.013 0.003 18.266
Metro 10 0.048 0.014 0.004 8.278
Metro 12 0.051 0.012 0.003 13.881
DEMetro_Z 0 0.047 0.015 0.006 5.000
DEMetro_Z 4 0.048 0.016 0.004 7.329
DEMetro_Z 6 0.057 0.014 0.005 8.720
DEMetro_Z 8 0.091 0.013 0.003 23.696
DEMetro_Z 10 0.069 0.014 0.004 13.286
DEMetro_Z 12 0.064 0.012 0.003 18.461
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.726 0.106 3.522
HMC 4 1.704 0.107 1.425
HMC 6 2.214 0.0367 0.676
HMC 8 0.350 0.73 0.103
HMC 10 1.782 0.0857 0.686
HMC 12 4.892 0.000176 5.492
SMC 0 0.642 0.527 0.205
SMC 4 1.969 0.0624 1.127
SMC 6 1.925 0.0645 0.739
SMC 8 3.721 0.00141 2.354
SMC 10 2.322 0.0327 1.857
SMC 12 2.659 0.0181 4.319
Metro 0 4.165 0.000822 5.595
Metro 4 3.535 0.00313 6.515
Metro 6 2.619 0.0144 1.102
Metro 8 2.652 0.0136 1.179
Metro 10 2.438 0.0253 1.748
Metro 12 3.541 0.00288 4.301
DEMetro_Z 0 2.656 0.017 2.407
DEMetro_Z 4 3.193 0.00539 2.715
DEMetro_Z 6 1.509 0.143 0.521
DEMetro_Z 8 1.449 0.166 1.387
DEMetro_Z 10 4.347 0.000168 1.675
DEMetro_Z 12 7.925 6.23e-07 7.883
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.482 0.637 0.124
HMC_vs_DEMetro_Z 1 -1.140 0.273 -0.294
HMC_vs_DEMetro_Z 2 0.586 0.567 0.151
HMC_vs_DEMetro_Z 3 -1.463 0.165 -0.378
HMC_vs_DEMetro_Z 4 -2.224 0.0431 -0.574
HMC_vs_DEMetro_Z 5 -1.448 0.17 -0.374
Metro_vs_SMC 0 4.135 0.00101 1.068
Metro_vs_SMC 1 2.715 0.0167 0.701
Metro_vs_SMC 2 0.805 0.434 0.208
Metro_vs_SMC 3 -1.923 0.075 -0.497
Metro_vs_SMC 4 -0.095 0.926 -0.024
Metro_vs_SMC 5 -0.015 0.988 -0.004
Metro_vs_DEMetro_Z 0 1.884 0.0805 0.486
Metro_vs_DEMetro_Z 1 1.649 0.121 0.426
Metro_vs_DEMetro_Z 2 1.312 0.211 0.339
Metro_vs_DEMetro_Z 3 -0.270 0.791 -0.070
Metro_vs_DEMetro_Z 4 0.093 0.927 0.024
Metro_vs_DEMetro_Z 5 -2.585 0.0216 -0.667
HMC_vs_Metro 0 -1.079 0.299 -0.279
HMC_vs_Metro 1 -2.358 0.0335 -0.609
HMC_vs_Metro 2 -1.104 0.288 -0.285
HMC_vs_Metro 3 -3.001 0.00954 -0.775
HMC_vs_Metro 4 -1.865 0.0833 -0.481
HMC_vs_Metro 5 0.607 0.554 0.157
HMC_vs_SMC 0 1.633 0.125 0.422
HMC_vs_SMC 1 0.297 0.771 0.077
HMC_vs_SMC 2 -0.200 0.845 -0.052
HMC_vs_SMC 3 -3.724 0.00227 -0.961
HMC_vs_SMC 4 -1.479 0.161 -0.382
HMC_vs_SMC 5 0.505 0.622 0.130
DEMetro_Z_vs_SMC 0 2.500 0.0255 0.645
DEMetro_Z_vs_SMC 1 1.808 0.0922 0.467
DEMetro_Z_vs_SMC 2 -0.536 0.601 -0.138
DEMetro_Z_vs_SMC 3 -1.096 0.292 -0.283
DEMetro_Z_vs_SMC 4 -0.220 0.829 -0.057
DEMetro_Z_vs_SMC 5 2.079 0.0565 0.537
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.193 0.053 0.040 3.522
HMC 4 0.102 0.054 0.033 1.425
HMC 6 0.157 0.083 0.111 0.676
HMC 8 0.108 0.091 0.165 0.103
HMC 10 0.116 0.069 0.067 0.686
HMC 12 0.246 0.053 0.035 5.492
SMC 0 0.061 0.053 0.040 0.205
SMC 4 0.092 0.054 0.033 1.127
SMC 6 0.164 0.083 0.111 0.739
SMC 8 0.480 0.091 0.165 2.354
SMC 10 0.195 0.069 0.067 1.857
SMC 12 0.205 0.053 0.035 4.319
Metro 0 0.275 0.053 0.040 5.595
Metro 4 0.270 0.054 0.033 6.515
Metro 6 0.204 0.083 0.111 1.102
Metro 8 0.286 0.091 0.165 1.179
Metro 10 0.187 0.069 0.067 1.748
Metro 12 0.204 0.053 0.035 4.301
DEMetro_Z 0 0.149 0.053 0.040 2.407
DEMetro_Z 4 0.144 0.054 0.033 2.715
DEMetro_Z 6 0.140 0.083 0.111 0.521
DEMetro_Z 8 0.320 0.091 0.165 1.387
DEMetro_Z 10 0.182 0.069 0.067 1.675
DEMetro_Z 12 0.330 0.053 0.035 7.883
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 0.516 0.612 0.354
HMC 4 2.286 0.0304 0.950
HMC 6 -1.056 0.309 -0.273
HMC 8 -0.551 0.588 -0.152
HMC 10 -0.974 0.345 -0.257
HMC 12 0.322 0.75 0.138
SMC 0 -0.919 0.374 -0.238
SMC 4 3.685 0.0022 5.106
SMC 6 -0.990 0.339 -0.256
SMC 8 -0.472 0.643 -0.130
SMC 10 -1.021 0.325 -0.264
SMC 12 -0.274 0.786 -0.097
Metro 0 -1.039 0.316 -0.268
Metro 4 2.544 0.0182 1.287
Metro 6 -1.077 0.3 -0.278
Metro 8 -0.531 0.602 -0.147
Metro 10 -0.982 0.342 -0.257
Metro 12 -0.053 0.958 -0.021
DEMetro_Z 0 -0.998 0.335 -0.259
DEMetro_Z 4 1.973 0.0605 0.977
DEMetro_Z 6 -1.071 0.302 -0.277
DEMetro_Z 8 -0.464 0.648 -0.128
DEMetro_Z 10 -1.068 0.303 -0.279
DEMetro_Z 12 0.507 0.617 0.203
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.928 0.369 0.239
HMC_vs_SMC 1 -3.167 0.00685 -0.818
HMC_vs_SMC 2 -1.992 0.0662 -0.514
HMC_vs_SMC 3 -1.325 0.206 -0.342
HMC_vs_SMC 4 0.137 0.893 0.035
HMC_vs_SMC 5 1.182 0.257 0.305
Metro_vs_DEMetro_Z 0 -0.526 0.607 -0.136
Metro_vs_DEMetro_Z 1 0.989 0.339 0.255
Metro_vs_DEMetro_Z 2 -0.637 0.534 -0.165
Metro_vs_DEMetro_Z 3 -0.753 0.464 -0.194
Metro_vs_DEMetro_Z 4 0.617 0.547 0.159
Metro_vs_DEMetro_Z 5 -1.479 0.161 -0.382
HMC_vs_Metro 0 0.980 0.344 0.253
HMC_vs_Metro 1 -0.845 0.412 -0.218
HMC_vs_Metro 2 0.818 0.427 0.211
HMC_vs_Metro 3 -0.665 0.517 -0.172
HMC_vs_Metro 4 -0.020 0.984 -0.005
HMC_vs_Metro 5 0.973 0.347 0.251
HMC_vs_DEMetro_Z 0 0.991 0.338 0.256
HMC_vs_DEMetro_Z 1 -0.082 0.936 -0.021
HMC_vs_DEMetro_Z 2 0.625 0.542 0.161
HMC_vs_DEMetro_Z 3 -0.942 0.362 -0.243
HMC_vs_DEMetro_Z 4 0.379 0.71 0.098
HMC_vs_DEMetro_Z 5 -0.385 0.706 -0.099
Metro_vs_SMC 0 -1.077 0.3 -0.278
Metro_vs_SMC 1 -2.693 0.0175 -0.695
Metro_vs_SMC 2 -4.036 0.00123 -1.042
Metro_vs_SMC 3 -1.010 0.33 -0.261
Metro_vs_SMC 4 0.185 0.856 0.048
Metro_vs_SMC 5 0.666 0.516 0.172
DEMetro_Z_vs_SMC 0 -0.590 0.564 -0.152
DEMetro_Z_vs_SMC 1 -2.923 0.0111 -0.755
DEMetro_Z_vs_SMC 2 -3.383 0.00446 -0.874
DEMetro_Z_vs_SMC 3 0.037 0.971 0.010
DEMetro_Z_vs_SMC 4 -0.299 0.769 -0.077
DEMetro_Z_vs_SMC 5 1.726 0.106 0.446
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 32.319 16.297 45.265 0.354
HMC 4 3.805 2.133 1.761 0.950
HMC 6 3.738 52.717 179.621 -0.273
HMC 8 45.469 105.394 394.325 -0.152
HMC 10 4.956 11.724 26.319 -0.257
HMC 12 5.023 4.249 5.608 0.138
SMC 0 5.522 16.297 45.265 -0.238
SMC 4 11.123 2.133 1.761 5.106
SMC 6 6.814 52.717 179.621 -0.256
SMC 8 54.323 105.394 394.325 -0.130
SMC 10 4.764 11.724 26.319 -0.264
SMC 12 3.704 4.249 5.608 -0.097
Metro 0 4.144 16.297 45.265 -0.268
Metro 4 4.399 2.133 1.761 1.287
Metro 6 2.749 52.717 179.621 -0.278
Metro 8 47.567 105.394 394.325 -0.147
Metro 10 4.970 11.724 26.319 -0.257
Metro 12 4.131 4.249 5.608 -0.021
DEMetro_Z 0 4.589 16.297 45.265 -0.259
DEMetro_Z 4 3.853 2.133 1.761 0.977
DEMetro_Z 6 3.025 52.717 179.621 -0.277
DEMetro_Z 8 54.788 105.394 394.325 -0.128
DEMetro_Z 10 4.377 11.724 26.319 -0.279
DEMetro_Z 12 5.386 4.249 5.608 0.203
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 1.972 0.0676 3.007
HMC 4 4.272 0.000559 3.960
HMC 6 2.276 0.033 0.672
HMC 8 2.215 0.0351 0.781
HMC 10 3.009 0.00688 1.785
HMC 12 6.086 2.04e-05 8.181
SMC 0 6.450 9.49e-06 7.497
SMC 4 4.277 0.00076 25.825
SMC 6 5.720 9.52e-06 3.035
SMC 8 5.657 4.34e-05 7.196
SMC 10 7.026 2.92e-06 7.106
SMC 12 5.471 7.16e-05 10.071
Metro 0 5.239 8.73e-05 5.748
Metro 4 6.005 2.83e-05 12.480
Metro 6 4.887 4e-05 1.662
Metro 8 4.329 0.000328 2.621
Metro 10 5.364 5.42e-05 4.614
Metro 12 5.191 0.000113 7.720
DEMetro_Z 0 5.088 4.61e-05 2.786
DEMetro_Z 4 5.723 3.64e-05 6.765
DEMetro_Z 6 3.583 0.00141 1.137
DEMetro_Z 8 2.144 0.0485 2.629
DEMetro_Z 10 5.655 2.67e-05 4.470
DEMetro_Z 12 12.285 1.3e-09 11.831
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 2.427 0.0293 0.627
Metro_vs_DEMetro_Z 1 2.453 0.0279 0.633
Metro_vs_DEMetro_Z 2 1.526 0.149 0.394
Metro_vs_DEMetro_Z 3 -0.008 0.993 -0.002
Metro_vs_DEMetro_Z 4 0.129 0.899 0.033
Metro_vs_DEMetro_Z 5 -2.573 0.0221 -0.664
DEMetro_Z_vs_SMC 0 -3.687 0.00244 -0.952
DEMetro_Z_vs_SMC 1 -2.977 0.01 -0.769
DEMetro_Z_vs_SMC 2 -3.465 0.00379 -0.895
DEMetro_Z_vs_SMC 3 -2.574 0.0221 -0.665
DEMetro_Z_vs_SMC 4 -3.158 0.00697 -0.816
DEMetro_Z_vs_SMC 5 0.844 0.413 0.218
HMC_vs_DEMetro_Z 0 0.138 0.892 0.036
HMC_vs_DEMetro_Z 1 -1.771 0.0983 -0.457
HMC_vs_DEMetro_Z 2 -1.810 0.0918 -0.467
HMC_vs_DEMetro_Z 3 -1.516 0.152 -0.391
HMC_vs_DEMetro_Z 4 -2.972 0.0101 -0.767
HMC_vs_DEMetro_Z 5 -2.030 0.0618 -0.524
HMC_vs_Metro 0 -3.428 0.00408 -0.885
HMC_vs_Metro 1 -3.688 0.00243 -0.952
HMC_vs_Metro 2 -4.174 0.000937 -1.078
HMC_vs_Metro 3 -3.187 0.00659 -0.823
HMC_vs_Metro 4 -4.850 0.000257 -1.252
HMC_vs_Metro 5 0.213 0.835 0.055
HMC_vs_SMC 0 -2.745 0.0158 -0.709
HMC_vs_SMC 1 -3.523 0.00337 -0.910
HMC_vs_SMC 2 -5.123 0.000155 -1.323
HMC_vs_SMC 3 -5.309 0.00011 -1.371
HMC_vs_SMC 4 -6.054 2.97e-05 -1.563
HMC_vs_SMC 5 -0.784 0.446 -0.202
Metro_vs_SMC 0 -1.189 0.254 -0.307
Metro_vs_SMC 1 -2.123 0.0521 -0.548
Metro_vs_SMC 2 -2.923 0.0111 -0.755
Metro_vs_SMC 3 -3.664 0.00255 -0.946
Metro_vs_SMC 4 -2.286 0.0383 -0.590
Metro_vs_SMC 5 -1.862 0.0837 -0.481
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.262 0.115 0.049 3.007
HMC 4 0.193 0.107 0.022 3.960
HMC 6 0.201 0.134 0.099 0.672
HMC 8 0.246 0.144 0.130 0.781
HMC 10 0.199 0.123 0.043 1.785
HMC 12 0.306 0.107 0.024 8.181
SMC 0 0.482 0.115 0.049 7.497
SMC 4 0.669 0.107 0.022 25.825
SMC 6 0.435 0.134 0.099 3.035
SMC 8 1.083 0.144 0.130 7.196
SMC 10 0.426 0.123 0.043 7.106
SMC 12 0.352 0.107 0.024 10.071
Metro 0 0.397 0.115 0.049 5.748
Metro 4 0.379 0.107 0.022 12.480
Metro 6 0.299 0.134 0.099 1.662
Metro 8 0.486 0.144 0.130 2.621
Metro 10 0.319 0.123 0.043 4.614
Metro 12 0.295 0.107 0.024 7.720
DEMetro_Z 0 0.251 0.115 0.049 2.786
DEMetro_Z 4 0.254 0.107 0.022 6.765
DEMetro_Z 6 0.247 0.134 0.099 1.137
DEMetro_Z 8 0.487 0.144 0.130 2.629
DEMetro_Z 10 0.313 0.123 0.043 4.470
DEMetro_Z 12 0.394 0.107 0.024 11.831
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0 4.795 7.54e-05 2.362
HMC 4 4.136 0.000586 2.820
HMC 6 7.073 2.48e-07 3.325
HMC 8 6.056 1.4e-05 5.286
HMC 10 5.154 9.58e-05 5.130
HMC 12 5.250 0.000117 16.207
SMC 0 6.546 1.15e-05 15.036
SMC 4 5.127 0.000152 27.249
SMC 6 6.692 9.28e-06 17.628
SMC 8 10.204 7.04e-08 62.669
SMC 10 5.383 9.29e-05 18.599
SMC 12 4.053 0.00118 25.472
Metro 0 8.087 5.99e-07 9.233
Metro 4 5.638 5.64e-05 13.905
Metro 6 7.585 1.11e-06 7.603
Metro 8 4.867 0.000243 19.304
Metro 10 7.946 6.55e-07 8.297
Metro 12 8.893 1.18e-07 8.315
DEMetro_Z 0 5.157 5.64e-05 3.387
DEMetro_Z 4 6.499 6.58e-06 6.001
DEMetro_Z 6 6.460 6.92e-06 5.873
DEMetro_Z 8 7.663 1.45e-06 10.621
DEMetro_Z 10 6.223 1.66e-05 8.923
DEMetro_Z 12 7.604 2.27e-06 24.443
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -4.833 0.000266 -1.248
DEMetro_Z_vs_SMC 1 -3.954 0.00144 -1.021
DEMetro_Z_vs_SMC 2 -4.141 0.001 -1.069
DEMetro_Z_vs_SMC 3 -8.380 7.95e-07 -2.164
DEMetro_Z_vs_SMC 4 -2.798 0.0142 -0.722
DEMetro_Z_vs_SMC 5 -0.127 0.901 -0.033
HMC_vs_Metro 0 -6.068 2.89e-05 -1.567
HMC_vs_Metro 1 -4.476 0.000522 -1.156
HMC_vs_Metro 2 -5.246 0.000124 -1.354
HMC_vs_Metro 3 -3.510 0.00347 -0.906
HMC_vs_Metro 4 -1.905 0.0775 -0.492
HMC_vs_Metro 5 2.251 0.041 0.581
Metro_vs_DEMetro_Z 0 4.782 0.000292 1.235
Metro_vs_DEMetro_Z 1 3.296 0.0053 0.851
Metro_vs_DEMetro_Z 2 1.483 0.16 0.383
Metro_vs_DEMetro_Z 3 2.590 0.0214 0.669
Metro_vs_DEMetro_Z 4 -0.363 0.722 -0.094
Metro_vs_DEMetro_Z 5 -5.099 0.000162 -1.317
HMC_vs_SMC 0 -5.582 6.76e-05 -1.441
HMC_vs_SMC 1 -4.464 0.000535 -1.152
HMC_vs_SMC 2 -5.356 0.000101 -1.383
HMC_vs_SMC 3 -9.103 2.95e-07 -2.350
HMC_vs_SMC 4 -4.393 0.000613 -1.134
HMC_vs_SMC 5 -1.308 0.212 -0.338
Metro_vs_SMC 0 -1.983 0.0673 -0.512
Metro_vs_SMC 1 -2.529 0.0241 -0.653
Metro_vs_SMC 2 -3.773 0.00206 -0.974
Metro_vs_SMC 3 -6.894 7.39e-06 -1.780
Metro_vs_SMC 4 -2.801 0.0142 -0.723
Metro_vs_SMC 5 -2.857 0.0127 -0.738
HMC_vs_DEMetro_Z 0 -1.419 0.178 -0.366
HMC_vs_DEMetro_Z 1 -2.977 0.01 -0.769
HMC_vs_DEMetro_Z 2 -2.560 0.0227 -0.661
HMC_vs_DEMetro_Z 3 -3.951 0.00145 -1.020
HMC_vs_DEMetro_Z 4 -2.691 0.0176 -0.695
HMC_vs_DEMetro_Z 5 -1.621 0.127 -0.418
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0 0.030 0.015 0.006 2.362
HMC 4 0.028 0.016 0.004 2.820
HMC 6 0.030 0.014 0.005 3.325
HMC 8 0.030 0.013 0.003 5.286
HMC 10 0.035 0.014 0.004 5.130
HMC 12 0.058 0.012 0.003 16.207
SMC 0 0.110 0.015 0.006 15.036
SMC 4 0.134 0.016 0.004 27.249
SMC 6 0.101 0.014 0.005 17.628
SMC 8 0.219 0.013 0.003 62.669
SMC 10 0.092 0.014 0.004 18.599
SMC 12 0.084 0.012 0.003 25.472
Metro 0 0.074 0.015 0.006 9.233
Metro 4 0.076 0.016 0.004 13.905
Metro 6 0.051 0.014 0.005 7.603
Metro 8 0.077 0.013 0.003 19.304
Metro 10 0.049 0.014 0.004 8.297
Metro 12 0.036 0.012 0.003 8.315
DEMetro_Z 0 0.037 0.015 0.006 3.387
DEMetro_Z 4 0.042 0.016 0.004 6.001
DEMetro_Z 6 0.043 0.014 0.005 5.873
DEMetro_Z 8 0.048 0.013 0.003 10.621
DEMetro_Z 10 0.051 0.014 0.004 8.923
DEMetro_Z 12 0.081 0.012 0.003 24.443
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
6 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
6 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0
4
6
8
10
12
Chain
0
4
6
8
10
12

three_attr_tails

▼

Varying_Tails_with_Dim_and_Corr (MvStudentT, nu, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.579 0.0215 5.923
HMC 2.5 3.579 0.0029 7.546
HMC 3.0 4.664 0.000333 8.998
HMC 4.0 4.882 0.000194 6.359
HMC 10.0 4.122 0.000972 8.324
HMC 50.0 5.340 9.61e-05 12.524
SMC 2.1 4.767 0.000255 7.035
SMC 2.5 5.759 4.65e-05 16.692
SMC 3.0 10.876 1.3e-08 13.107
SMC 4.0 5.603 5.82e-05 11.822
SMC 10.0 6.451 1.4e-05 18.158
SMC 50.0 6.495 1.28e-05 16.367
Metro 2.1 3.055 0.00856 891.057
Metro 2.5 4.905 0.000232 1133.181
Metro 3.0 5.728 5.23e-05 629.031
Metro 4.0 3.610 0.00284 174.409
Metro 10.0 5.514 7.63e-05 171.920
Metro 50.0 7.961 1.44e-06 116.846
DEMetro_Z 2.1 7.450 3.11e-06 659.754
DEMetro_Z 2.5 7.763 1.94e-06 2214.427
DEMetro_Z 3.0 6.053 2.97e-05 731.837
DEMetro_Z 4.0 8.532 6.34e-07 77.677
DEMetro_Z 10.0 7.641 2.32e-06 156.971
DEMetro_Z 50.0 5.934 3.65e-05 246.256
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -7.440 3.16e-06 -1.921
HMC_vs_DEMetro_Z 1 -7.725 2.05e-06 -1.995
HMC_vs_DEMetro_Z 2 -5.933 3.66e-05 -1.532
HMC_vs_DEMetro_Z 3 -7.551 2.67e-06 -1.950
HMC_vs_DEMetro_Z 4 -7.019 6.07e-06 -1.812
HMC_vs_DEMetro_Z 5 -5.725 5.25e-05 -1.478
Metro_vs_SMC 0 3.033 0.00894 0.783
Metro_vs_SMC 1 4.854 0.000255 1.253
Metro_vs_SMC 2 5.618 6.34e-05 1.451
Metro_vs_SMC 3 3.319 0.00507 0.857
Metro_vs_SMC 4 4.874 0.000246 1.259
Metro_vs_SMC 5 6.746 9.38e-06 1.742
Metro_vs_DEMetro_Z 0 0.700 0.496 0.181
Metro_vs_DEMetro_Z 1 -3.702 0.00237 -0.956
Metro_vs_DEMetro_Z 2 -0.811 0.431 -0.209
Metro_vs_DEMetro_Z 3 2.166 0.048 0.559
Metro_vs_DEMetro_Z 4 0.433 0.671 0.112
Metro_vs_DEMetro_Z 5 -2.921 0.0112 -0.754
HMC_vs_Metro 0 -3.029 0.00902 -0.782
HMC_vs_Metro 1 -4.872 0.000247 -1.258
HMC_vs_Metro 2 -5.609 6.44e-05 -1.448
HMC_vs_Metro 3 -3.480 0.00368 -0.899
HMC_vs_Metro 4 -5.198 0.000135 -1.342
HMC_vs_Metro 5 -6.749 9.33e-06 -1.743
HMC_vs_SMC 0 -0.454 0.657 -0.117
HMC_vs_SMC 1 -3.157 0.007 -0.815
HMC_vs_SMC 2 -1.639 0.124 -0.423
HMC_vs_SMC 3 -2.016 0.0634 -0.521
HMC_vs_SMC 4 -3.413 0.0042 -0.881
HMC_vs_SMC 5 -0.944 0.361 -0.244
DEMetro_Z_vs_SMC 0 7.363 3.55e-06 1.901
DEMetro_Z_vs_SMC 1 7.715 2.08e-06 1.992
DEMetro_Z_vs_SMC 2 5.969 3.44e-05 1.541
DEMetro_Z_vs_SMC 3 6.682 1.04e-05 1.725
DEMetro_Z_vs_SMC 4 6.286 2e-05 1.623
DEMetro_Z_vs_SMC 5 5.458 8.44e-05 1.409
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.299 0.068 0.039 5.923
HMC 2.5 0.205 0.037 0.022 7.546
HMC 3.0 0.212 0.031 0.020 8.998
HMC 4.0 0.175 0.029 0.023 6.359
HMC 10.0 0.150 0.019 0.016 8.324
HMC 50.0 0.137 0.014 0.010 12.524
SMC 2.1 0.343 0.068 0.039 7.035
SMC 2.5 0.409 0.037 0.022 16.692
SMC 3.0 0.294 0.031 0.020 13.107
SMC 4.0 0.300 0.029 0.023 11.822
SMC 10.0 0.305 0.019 0.016 18.158
SMC 50.0 0.174 0.014 0.010 16.367
Metro 2.1 34.923 0.068 0.039 891.057
Metro 2.5 25.323 0.037 0.022 1133.181
Metro 3.0 12.655 0.031 0.020 629.031
Metro 4.0 4.020 0.029 0.023 174.409
Metro 10.0 2.728 0.019 0.016 171.920
Metro 50.0 1.162 0.014 0.010 116.846
DEMetro_Z 2.1 25.875 0.068 0.039 659.754
DEMetro_Z 2.5 49.450 0.037 0.022 2214.427
DEMetro_Z 3.0 14.718 0.031 0.020 731.837
DEMetro_Z 4.0 1.807 0.029 0.023 77.677
DEMetro_Z 10.0 2.493 0.019 0.016 156.971
DEMetro_Z 50.0 2.434 0.014 0.010 246.256
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.541 0.593 0.211
HMC 2.5 1.092 0.284 0.361
HMC 3.0 0.934 0.359 0.335
HMC 4.0 5.506 5.36e-05 6.277
HMC 10.0 4.150 0.00093 9.172
HMC 50.0 3.475 0.00348 5.608
SMC 2.1 25.396 1.49e-16 15.591
SMC 2.5 33.465 6.52e-15 102.822
SMC 3.0 30.002 3.84e-14 182.610
SMC 4.0 30.028 4.11e-14 1994.702
SMC 10.0 28.325 9.21e-14 4635.733
SMC 50.0 36.724 2.48e-15 424.772
Metro 2.1 2.458 0.0276 751.824
Metro 2.5 6.255 2.11e-05 1766.620
Metro 3.0 3.428 0.00408 1069.848
Metro 4.0 1.983 0.0673 950.081
Metro 10.0 3.175 0.00675 1290.522
Metro 50.0 2.795 0.0143 312.647
DEMetro_Z 2.1 9.165 2.72e-07 280.621
DEMetro_Z 2.5 7.581 2.55e-06 1692.126
DEMetro_Z 3.0 10.619 4.41e-08 591.933
DEMetro_Z 4.0 6.109 2.7e-05 474.547
DEMetro_Z 10.0 8.516 6.57e-07 1274.097
DEMetro_Z 50.0 5.990 3.31e-05 1184.502
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -22.343 2.38e-12 -5.769
HMC_vs_SMC 1 -33.528 8.98e-15 -8.657
HMC_vs_SMC 2 -29.531 5.18e-14 -7.625
HMC_vs_SMC 3 -29.807 4.56e-14 -7.696
HMC_vs_SMC 4 -28.055 1.05e-13 -7.244
HMC_vs_SMC 5 -37.162 2.16e-15 -9.595
Metro_vs_DEMetro_Z 0 1.518 0.151 0.392
Metro_vs_DEMetro_Z 1 0.196 0.847 0.051
Metro_vs_DEMetro_Z 2 1.485 0.16 0.383
Metro_vs_DEMetro_Z 3 1.014 0.328 0.262
Metro_vs_DEMetro_Z 4 0.040 0.968 0.010
Metro_vs_DEMetro_Z 5 -4.491 0.000508 -1.160
HMC_vs_Metro 0 -2.457 0.0277 -0.634
HMC_vs_Metro 1 -6.255 2.11e-05 -1.615
HMC_vs_Metro 2 -3.427 0.00408 -0.885
HMC_vs_Metro 3 -1.972 0.0688 -0.509
HMC_vs_Metro 4 -3.151 0.00708 -0.814
HMC_vs_Metro 5 -2.753 0.0156 -0.711
HMC_vs_DEMetro_Z 0 -9.178 2.67e-07 -2.370
HMC_vs_DEMetro_Z 1 -7.580 2.55e-06 -1.957
HMC_vs_DEMetro_Z 2 -10.621 4.41e-08 -2.742
HMC_vs_DEMetro_Z 3 -6.009 3.21e-05 -1.551
HMC_vs_DEMetro_Z 4 -8.464 7.06e-07 -2.185
HMC_vs_DEMetro_Z 5 -5.950 3.54e-05 -1.536
Metro_vs_SMC 0 2.406 0.0305 0.621
Metro_vs_SMC 1 5.869 4.08e-05 1.515
Metro_vs_SMC 2 2.835 0.0132 0.732
Metro_vs_SMC 3 -2.027 0.0622 -0.523
Metro_vs_SMC 4 -7.705 2.12e-06 -1.989
Metro_vs_SMC 5 -0.994 0.337 -0.257
DEMetro_Z_vs_SMC 0 8.580 6.01e-07 2.215
DEMetro_Z_vs_SMC 1 7.127 5.12e-06 1.840
DEMetro_Z_vs_SMC 2 7.490 2.92e-06 1.934
DEMetro_Z_vs_SMC 3 -12.728 4.38e-09 -3.286
DEMetro_Z_vs_SMC 4 -15.177 4.36e-10 -3.919
DEMetro_Z_vs_SMC 5 3.890 0.00163 1.004
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 8.310 5.634 12.695 0.211
HMC 2.5 2.312 1.663 1.796 0.361
HMC 3.0 1.205 0.857 1.037 0.335
HMC 4.0 0.660 0.123 0.086 6.277
HMC 10.0 0.254 0.038 0.024 9.172
HMC 50.0 0.128 0.029 0.018 5.608
SMC 2.1 203.551 5.634 12.695 15.591
SMC 2.5 186.350 1.663 1.796 102.822
SMC 3.0 190.159 0.857 1.037 182.610
SMC 4.0 170.782 0.123 0.086 1994.702
SMC 10.0 109.331 0.038 0.024 4635.733
SMC 50.0 7.520 0.029 0.018 424.772
Metro 2.1 9549.785 5.634 12.695 751.824
Metro 2.5 3174.834 1.663 1.796 1766.620
Metro 3.0 1109.909 0.857 1.037 1069.848
Metro 4.0 81.408 0.123 0.086 950.081
Metro 10.0 30.463 0.038 0.024 1290.522
Metro 50.0 5.542 0.029 0.018 312.647
DEMetro_Z 2.1 3568.029 5.634 12.695 280.621
DEMetro_Z 2.5 3041.028 1.663 1.796 1692.126
DEMetro_Z 3.0 614.481 0.857 1.037 591.933
DEMetro_Z 4.0 40.724 0.123 0.086 474.547
DEMetro_Z 10.0 30.076 0.038 0.024 1274.097
DEMetro_Z 50.0 20.916 0.029 0.018 1184.502
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.311 0.00509 12.845
HMC 2.5 10.063 5.01e-08 15.034
HMC 3.0 7.749 1.5e-06 13.513
HMC 4.0 6.975 5.23e-06 12.737
HMC 10.0 5.786 4.38e-05 15.235
HMC 50.0 6.448 1.46e-05 24.705
SMC 2.1 62.245 1.41e-18 329.638
SMC 2.5 63.554 1.18e-18 624.869
SMC 3.0 63.059 1.31e-18 622.868
SMC 4.0 66.949 5.74e-19 748.938
SMC 10.0 52.518 1.73e-17 808.178
SMC 50.0 47.430 6.61e-17 302.882
Metro 2.1 5.547 7.19e-05 1799.560
Metro 2.5 11.178 2.31e-08 2632.505
Metro 3.0 7.700 2.13e-06 1218.482
Metro 4.0 5.449 8.57e-05 396.586
Metro 10.0 8.142 1.11e-06 439.809
Metro 50.0 8.586 5.95e-07 297.267
DEMetro_Z 2.1 22.227 2.56e-12 1604.487
DEMetro_Z 2.5 14.451 8.33e-10 3683.845
DEMetro_Z 3.0 15.557 3.14e-10 1393.839
DEMetro_Z 4.0 13.256 2.58e-09 344.683
DEMetro_Z 10.0 15.794 2.56e-10 467.860
DEMetro_Z 50.0 9.910 1.04e-07 793.851
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.542 0.596 0.140
Metro_vs_DEMetro_Z 1 -3.298 0.00528 -0.852
Metro_vs_DEMetro_Z 2 -0.951 0.358 -0.245
Metro_vs_DEMetro_Z 3 0.713 0.488 0.184
Metro_vs_DEMetro_Z 4 -0.576 0.574 -0.149
Metro_vs_DEMetro_Z 5 -5.628 6.23e-05 -1.453
DEMetro_Z_vs_SMC 0 17.193 8.27e-11 4.439
DEMetro_Z_vs_SMC 1 11.899 1.04e-08 3.072
DEMetro_Z_vs_SMC 2 9.198 2.6e-07 2.375
DEMetro_Z_vs_SMC 3 -12.057 8.8e-09 -3.113
DEMetro_Z_vs_SMC 4 -9.265 2.38e-07 -2.392
DEMetro_Z_vs_SMC 5 6.234 2.18e-05 1.610
HMC_vs_DEMetro_Z 0 -22.645 1.98e-12 -5.847
HMC_vs_DEMetro_Z 1 -14.358 9.07e-10 -3.707
HMC_vs_DEMetro_Z 2 -15.393 3.61e-10 -3.974
HMC_vs_DEMetro_Z 3 -12.396 6.16e-09 -3.201
HMC_vs_DEMetro_Z 4 -15.416 3.54e-10 -3.980
HMC_vs_DEMetro_Z 5 -9.559 1.63e-07 -2.468
HMC_vs_Metro 0 -5.479 8.12e-05 -1.415
HMC_vs_Metro 1 -11.104 2.52e-08 -2.867
HMC_vs_Metro 2 -7.605 2.46e-06 -1.964
HMC_vs_Metro 3 -5.254 0.000122 -1.357
HMC_vs_Metro 4 -7.770 1.92e-06 -2.006
HMC_vs_Metro 5 -7.589 2.52e-06 -1.959
HMC_vs_SMC 0 -41.858 4.13e-16 -10.808
HMC_vs_SMC 1 -60.283 2.57e-18 -15.565
HMC_vs_SMC 2 -59.792 2.88e-18 -15.438
HMC_vs_SMC 3 -64.048 1.1e-18 -16.537
HMC_vs_SMC 4 -49.485 4.03e-17 -12.777
HMC_vs_SMC 5 -33.840 7.9e-15 -8.737
Metro_vs_SMC 0 4.519 0.000481 1.167
Metro_vs_SMC 1 8.439 7.31e-07 2.179
Metro_vs_SMC 2 3.787 0.002 0.978
Metro_vs_SMC 3 -4.446 0.000554 -1.148
Metro_vs_SMC 4 -6.563 1.26e-05 -1.694
Metro_vs_SMC 5 -0.161 0.875 -0.041
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.477 0.102 0.029 12.845
HMC 2.5 0.289 0.066 0.015 15.034
HMC 3.0 0.261 0.058 0.015 13.513
HMC 4.0 0.192 0.043 0.012 12.737
HMC 10.0 0.155 0.028 0.008 15.235
HMC 50.0 0.129 0.024 0.004 24.705
SMC 2.1 9.726 0.102 0.029 329.638
SMC 2.5 9.348 0.066 0.015 624.869
SMC 3.0 9.384 0.058 0.015 622.868
SMC 4.0 8.805 0.043 0.012 748.938
SMC 10.0 6.739 0.028 0.008 808.178
SMC 50.0 1.314 0.024 0.004 302.882
Metro 2.1 52.640 0.102 0.029 1799.560
Metro 2.5 39.169 0.066 0.015 2632.505
Metro 3.0 18.302 0.058 0.015 1218.482
Metro 4.0 4.682 0.043 0.012 396.586
Metro 10.0 3.680 0.028 0.008 439.809
Metro 50.0 1.290 0.024 0.004 297.267
DEMetro_Z 2.1 46.945 0.102 0.029 1604.487
DEMetro_Z 2.5 54.786 0.066 0.015 3683.845
DEMetro_Z 3.0 20.927 0.058 0.015 1393.839
DEMetro_Z 4.0 4.075 0.043 0.012 344.683
DEMetro_Z 10.0 3.913 0.028 0.008 467.860
DEMetro_Z 50.0 3.406 0.024 0.004 793.851
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.971 0.000191 11.618
HMC 2.5 7.077 5.2e-06 24.194
HMC 3.0 6.608 9.99e-06 13.431
HMC 4.0 7.309 3.16e-06 14.444
HMC 10.0 8.174 7.67e-07 13.704
HMC 50.0 6.681 9.2e-06 15.580
SMC 2.1 75.505 1.33e-21 79.963
SMC 2.5 135.607 1.16e-24 183.497
SMC 3.0 81.004 5.36e-22 87.604
SMC 4.0 56.274 2.67e-18 120.647
SMC 10.0 82.007 9.1e-22 96.748
SMC 50.0 65.111 1.65e-19 107.519
Metro 2.1 43.805 1.25e-16 113.423
Metro 2.5 30.580 3.08e-14 273.884
Metro 3.0 28.825 6.07e-14 118.719
Metro 4.0 14.193 1.04e-09 138.412
Metro 10.0 14.067 1.16e-09 121.535
Metro 50.0 14.106 1.12e-09 119.208
DEMetro_Z 2.1 38.889 7.09e-16 105.409
DEMetro_Z 2.5 20.224 9.12e-12 268.282
DEMetro_Z 3.0 26.040 2.5e-13 109.231
DEMetro_Z 4.0 25.744 3.04e-13 123.785
DEMetro_Z 10.0 29.952 3.33e-14 105.088
DEMetro_Z 50.0 21.659 3.5e-12 169.878
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 10.039 8.9e-08 2.592
DEMetro_Z_vs_SMC 1 6.210 2.27e-05 1.603
DEMetro_Z_vs_SMC 2 5.348 0.000103 1.381
DEMetro_Z_vs_SMC 3 0.639 0.533 0.165
DEMetro_Z_vs_SMC 4 2.276 0.0391 0.588
DEMetro_Z_vs_SMC 5 7.793 1.86e-06 2.012
HMC_vs_Metro 0 -26.047 2.92e-13 -6.725
HMC_vs_Metro 1 -34.418 6.25e-15 -8.887
HMC_vs_Metro 2 -26.677 2.1e-13 -6.888
HMC_vs_Metro 3 -13.465 2.1e-09 -3.477
HMC_vs_Metro 4 -12.973 3.42e-09 -3.350
HMC_vs_Metro 5 -11.763 1.21e-08 -3.037
Metro_vs_DEMetro_Z 0 2.123 0.0521 0.548
Metro_vs_DEMetro_Z 1 0.317 0.756 0.082
Metro_vs_DEMetro_Z 2 1.625 0.126 0.420
Metro_vs_DEMetro_Z 3 1.194 0.252 0.308
Metro_vs_DEMetro_Z 4 1.814 0.0911 0.468
Metro_vs_DEMetro_Z 5 -4.372 0.000638 -1.129
HMC_vs_SMC 0 -26.925 1.85e-13 -6.952
HMC_vs_SMC 1 -39.807 8.31e-16 -10.278
HMC_vs_SMC 2 -35.615 3.89e-15 -9.196
HMC_vs_SMC 3 -36.180 3.13e-15 -9.342
HMC_vs_SMC 4 -35.530 4.02e-15 -9.174
HMC_vs_SMC 5 -33.397 9.48e-15 -8.623
Metro_vs_SMC 0 14.231 1.02e-09 3.674
Metro_vs_SMC 1 10.265 6.75e-08 2.650
Metro_vs_SMC 2 8.604 5.81e-07 2.222
Metro_vs_SMC 3 1.671 0.117 0.431
Metro_vs_SMC 4 2.769 0.0151 0.715
Metro_vs_SMC 5 1.318 0.209 0.340
HMC_vs_DEMetro_Z 0 -30.169 3.86e-14 -7.790
HMC_vs_DEMetro_Z 1 -17.747 5.4e-11 -4.582
HMC_vs_DEMetro_Z 2 -19.970 1.1e-11 -5.156
HMC_vs_DEMetro_Z 3 -18.167 3.94e-11 -4.691
HMC_vs_DEMetro_Z 4 -23.494 1.2e-12 -6.066
HMC_vs_DEMetro_Z 5 -19.731 1.29e-11 -5.094
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.084 0.016 0.006 11.618
HMC 2.5 0.078 0.015 0.003 24.194
HMC 3.0 0.091 0.015 0.006 13.431
HMC 4.0 0.074 0.014 0.004 14.444
HMC 10.0 0.092 0.014 0.006 13.704
HMC 50.0 0.073 0.015 0.004 15.580
SMC 2.1 0.484 0.016 0.006 79.963
SMC 2.5 0.491 0.015 0.003 183.497
SMC 3.0 0.508 0.015 0.006 87.604
SMC 4.0 0.516 0.014 0.004 120.647
SMC 10.0 0.560 0.014 0.006 96.748
SMC 50.0 0.420 0.015 0.004 107.519
Metro 2.1 0.681 0.016 0.006 113.423
Metro 2.5 0.726 0.015 0.003 273.884
Metro 3.0 0.683 0.015 0.006 118.719
Metro 4.0 0.590 0.014 0.004 138.412
Metro 10.0 0.700 0.014 0.006 121.535
Metro 50.0 0.464 0.015 0.004 119.208
DEMetro_Z 2.1 0.634 0.016 0.006 105.409
DEMetro_Z 2.5 0.712 0.015 0.003 268.282
DEMetro_Z 3.0 0.630 0.015 0.006 109.231
DEMetro_Z 4.0 0.529 0.014 0.004 123.785
DEMetro_Z 10.0 0.607 0.014 0.006 105.088
DEMetro_Z 50.0 0.654 0.015 0.004 169.878
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.300 0.00495 5.252
HMC 2.5 3.309 0.00505 8.619
HMC 3.0 5.408 8.15e-05 10.460
HMC 4.0 4.148 0.000808 4.799
HMC 10.0 5.588 5.36e-05 8.352
HMC 50.0 4.036 0.00119 11.735
SMC 2.1 6.001 2.58e-05 9.391
SMC 2.5 7.063 5.27e-06 22.710
SMC 3.0 5.676 5.63e-05 32.253
SMC 4.0 6.482 1.33e-05 17.855
SMC 10.0 4.837 0.000259 21.163
SMC 50.0 5.049 0.00017 15.308
Metro 2.1 4.133 0.00101 645.407
Metro 2.5 3.524 0.00337 2339.196
Metro 3.0 1.461 0.166 1052.095
Metro 4.0 4.165 0.000953 128.889
Metro 10.0 4.400 0.000605 156.225
Metro 50.0 5.620 6.31e-05 175.153
DEMetro_Z 2.1 8.038 1.3e-06 728.436
DEMetro_Z 2.5 6.015 3.17e-05 3167.592
DEMetro_Z 3.0 6.409 1.63e-05 1167.400
DEMetro_Z 4.0 5.653 5.96e-05 208.434
DEMetro_Z 10.0 5.264 0.00012 290.831
DEMetro_Z 50.0 6.701 1.01e-05 345.643
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -7.960 1.45e-06 -2.055
HMC_vs_DEMetro_Z 1 -5.993 3.3e-05 -1.547
HMC_vs_DEMetro_Z 2 -6.338 1.84e-05 -1.636
HMC_vs_DEMetro_Z 3 -5.569 6.91e-05 -1.438
HMC_vs_DEMetro_Z 4 -5.121 0.000156 -1.322
HMC_vs_DEMetro_Z 5 -6.681 1.04e-05 -1.725
Metro_vs_SMC 0 4.086 0.00111 1.055
Metro_vs_SMC 1 3.483 0.00365 0.899
Metro_vs_SMC 2 1.416 0.179 0.366
Metro_vs_SMC 3 3.617 0.0028 0.934
Metro_vs_SMC 4 3.675 0.0025 0.949
Metro_vs_SMC 5 5.006 0.000192 1.293
Metro_vs_DEMetro_Z 0 -0.405 0.691 -0.105
Metro_vs_DEMetro_Z 1 -1.464 0.165 -0.378
Metro_vs_DEMetro_Z 2 -0.166 0.871 -0.043
Metro_vs_DEMetro_Z 3 -1.589 0.134 -0.410
Metro_vs_DEMetro_Z 4 -1.924 0.0749 -0.497
Metro_vs_DEMetro_Z 5 -3.721 0.00228 -0.961
HMC_vs_Metro 0 -4.102 0.00108 -1.059
HMC_vs_Metro 1 -3.506 0.0035 -0.905
HMC_vs_Metro 2 -1.448 0.17 -0.374
HMC_vs_Metro 3 -3.923 0.00153 -1.013
HMC_vs_Metro 4 -4.159 0.000964 -1.074
HMC_vs_Metro 5 -5.555 7.1e-05 -1.434
HMC_vs_SMC 0 -2.301 0.0373 -0.594
HMC_vs_SMC 1 -4.922 0.000225 -1.271
HMC_vs_SMC 2 -4.276 0.000769 -1.104
HMC_vs_SMC 3 -4.091 0.0011 -1.056
HMC_vs_SMC 4 -3.112 0.00765 -0.803
HMC_vs_SMC 5 -0.759 0.46 -0.196
DEMetro_Z_vs_SMC 0 7.928 1.52e-06 2.047
DEMetro_Z_vs_SMC 1 5.964 3.46e-05 1.540
DEMetro_Z_vs_SMC 2 6.231 2.2e-05 1.609
DEMetro_Z_vs_SMC 3 5.193 0.000136 1.341
DEMetro_Z_vs_SMC 4 4.845 0.000259 1.251
DEMetro_Z_vs_SMC 5 6.284 2.01e-05 1.622
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.273 0.068 0.039 5.252
HMC 2.5 0.229 0.037 0.022 8.619
HMC 3.0 0.241 0.031 0.020 10.460
HMC 4.0 0.139 0.029 0.023 4.799
HMC 10.0 0.151 0.019 0.016 8.352
HMC 50.0 0.129 0.014 0.010 11.735
SMC 2.1 0.435 0.068 0.039 9.391
SMC 2.5 0.544 0.037 0.022 22.710
SMC 3.0 0.678 0.031 0.020 32.253
SMC 4.0 0.438 0.029 0.023 17.855
SMC 10.0 0.352 0.019 0.016 21.163
SMC 50.0 0.164 0.014 0.010 15.308
Metro 2.1 25.314 0.068 0.039 645.407
Metro 2.5 52.235 0.037 0.022 2339.196
Metro 3.0 21.145 0.031 0.020 1052.095
Metro 4.0 2.979 0.029 0.023 128.889
Metro 10.0 2.481 0.019 0.016 156.225
Metro 50.0 1.735 0.014 0.010 175.153
DEMetro_Z 2.1 28.562 0.068 0.039 728.436
DEMetro_Z 2.5 70.720 0.037 0.022 3167.592
DEMetro_Z 3.0 23.459 0.031 0.020 1167.400
DEMetro_Z 4.0 4.799 0.029 0.023 208.434
DEMetro_Z 10.0 4.602 0.019 0.016 290.831
DEMetro_Z 50.0 3.412 0.014 0.010 345.643
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.775 0.445 0.318
HMC 2.5 1.415 0.172 0.857
HMC 3.0 2.442 0.0224 1.165
HMC 4.0 3.045 0.00815 4.116
HMC 10.0 3.779 0.00174 4.410
HMC 50.0 5.924 2.81e-05 8.310
SMC 2.1 10.277 5.72e-08 29.442
SMC 2.5 14.695 6.62e-10 219.416
SMC 3.0 14.184 1.06e-09 387.343
SMC 4.0 11.881 1.06e-08 4706.811
SMC 10.0 38.668 1.24e-15 8062.364
SMC 50.0 27.282 1.53e-13 477.923
Metro 2.1 2.935 0.0109 55.352
Metro 2.5 3.052 0.00861 1177.377
Metro 3.0 1.013 0.328 1396.213
Metro 4.0 2.401 0.0308 74.416
Metro 10.0 3.980 0.00137 59.474
Metro 50.0 4.748 0.000309 31.855
DEMetro_Z 2.1 7.843 1.7e-06 63.146
DEMetro_Z 2.5 7.123 5.15e-06 330.638
DEMetro_Z 3.0 5.800 4.6e-05 184.296
DEMetro_Z 4.0 4.185 0.000916 61.521
DEMetro_Z 10.0 5.559 7.03e-05 122.766
DEMetro_Z 50.0 4.607 0.000407 96.208
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -10.796 3.59e-08 -2.787
HMC_vs_SMC 1 -14.979 5.19e-10 -3.867
HMC_vs_SMC 2 -14.054 1.2e-09 -3.629
HMC_vs_SMC 3 -11.877 1.07e-08 -3.067
HMC_vs_SMC 4 -38.572 1.29e-15 -9.959
HMC_vs_SMC 5 -27.586 1.33e-13 -7.123
Metro_vs_DEMetro_Z 0 -0.364 0.721 -0.094
Metro_vs_DEMetro_Z 1 2.140 0.0504 0.553
Metro_vs_DEMetro_Z 2 0.875 0.396 0.226
Metro_vs_DEMetro_Z 3 0.334 0.743 0.086
Metro_vs_DEMetro_Z 4 -2.552 0.023 -0.659
Metro_vs_DEMetro_Z 5 -3.290 0.00536 -0.850
HMC_vs_Metro 0 -2.918 0.0112 -0.753
HMC_vs_Metro 1 -3.050 0.00866 -0.787
HMC_vs_Metro 2 -1.012 0.329 -0.261
HMC_vs_Metro 3 -2.274 0.0392 -0.587
HMC_vs_Metro 4 -3.654 0.0026 -0.944
HMC_vs_Metro 5 -3.478 0.00369 -0.898
HMC_vs_DEMetro_Z 0 -7.779 1.89e-06 -2.009
HMC_vs_DEMetro_Z 1 -7.101 5.33e-06 -1.834
HMC_vs_DEMetro_Z 2 -5.753 5e-05 -1.485
HMC_vs_DEMetro_Z 3 -3.856 0.00175 -0.996
HMC_vs_DEMetro_Z 4 -5.264 0.00012 -1.359
HMC_vs_DEMetro_Z 5 -4.149 0.000983 -1.071
Metro_vs_SMC 0 1.299 0.215 0.336
Metro_vs_SMC 1 2.483 0.0263 0.641
Metro_vs_SMC 2 0.731 0.477 0.189
Metro_vs_SMC 3 -11.964 9.72e-09 -3.089
Metro_vs_SMC 4 -39.825 8.26e-16 -10.283
Metro_vs_SMC 5 -21.901 3.13e-12 -5.655
DEMetro_Z_vs_SMC 0 3.831 0.00183 0.989
DEMetro_Z_vs_SMC 1 2.225 0.0431 0.574
DEMetro_Z_vs_SMC 2 -4.550 0.000454 -1.175
DEMetro_Z_vs_SMC 3 -11.542 1.54e-08 -2.980
DEMetro_Z_vs_SMC 4 -38.685 1.24e-15 -9.989
DEMetro_Z_vs_SMC 5 -11.952 9.85e-09 -3.086
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 9.672 5.634 12.695 0.318
HMC 2.5 3.203 1.663 1.796 0.857
HMC 3.0 2.065 0.857 1.037 1.165
HMC 4.0 0.475 0.123 0.086 4.116
HMC 10.0 0.142 0.038 0.024 4.410
HMC 50.0 0.176 0.029 0.018 8.310
SMC 2.1 379.393 5.634 12.695 29.442
SMC 2.5 395.774 1.663 1.796 219.416
SMC 3.0 402.394 0.857 1.037 387.343
SMC 4.0 402.820 0.123 0.086 4706.811
SMC 10.0 190.118 0.038 0.024 8062.364
SMC 50.0 8.457 0.029 0.018 477.923
Metro 2.1 708.306 5.634 12.695 55.352
Metro 2.5 2116.446 1.663 1.796 1177.377
Metro 3.0 1448.232 0.857 1.037 1396.213
Metro 4.0 6.490 0.123 0.086 74.416
Metro 10.0 1.440 0.038 0.024 59.474
Metro 50.0 0.591 0.029 0.018 31.855
DEMetro_Z 2.1 807.256 5.634 12.695 63.146
DEMetro_Z 2.5 595.549 1.663 1.796 330.638
DEMetro_Z 3.0 191.907 0.857 1.037 184.296
DEMetro_Z 4.0 5.387 0.123 0.086 61.521
DEMetro_Z 10.0 2.932 0.038 0.024 122.766
DEMetro_Z 50.0 1.726 0.029 0.018 96.208
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.535 6.68e-05 12.439
HMC 2.5 4.301 0.000722 20.279
HMC 3.0 5.907 3.57e-05 16.670
HMC 4.0 7.443 2.21e-06 11.247
HMC 10.0 7.280 3.22e-06 13.530
HMC 50.0 5.148 0.000145 24.807
SMC 2.1 21.069 5.27e-12 435.942
SMC 2.5 27.481 1.39e-13 888.578
SMC 3.0 26.791 1.98e-13 891.427
SMC 4.0 22.401 2.3e-12 1122.116
SMC 10.0 59.729 2.88e-18 1038.066
SMC 50.0 35.149 4.49e-15 324.580
Metro 2.1 4.604 0.000409 787.366
Metro 2.5 3.664 0.00256 3014.570
Metro 3.0 1.450 0.169 1141.280
Metro 4.0 4.575 0.000433 223.233
Metro 10.0 4.621 0.000396 240.796
Metro 50.0 5.496 7.88e-05 333.458
DEMetro_Z 2.1 14.119 1.13e-09 1050.258
DEMetro_Z 2.5 6.788 8.76e-06 4067.757
DEMetro_Z 3.0 8.107 1.17e-06 1428.961
DEMetro_Z 4.0 6.314 1.91e-05 358.437
DEMetro_Z 10.0 5.892 3.92e-05 469.562
DEMetro_Z 50.0 7.252 4.21e-06 668.479
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.204 0.249 -0.311
Metro_vs_DEMetro_Z 1 -1.504 0.155 -0.388
Metro_vs_DEMetro_Z 2 -0.375 0.713 -0.097
Metro_vs_DEMetro_Z 3 -1.723 0.107 -0.445
Metro_vs_DEMetro_Z 4 -2.314 0.0364 -0.597
Metro_vs_DEMetro_Z 5 -4.103 0.00108 -1.059
DEMetro_Z_vs_SMC 0 7.940 1.49e-06 2.050
DEMetro_Z_vs_SMC 1 5.295 0.000113 1.367
DEMetro_Z_vs_SMC 2 2.912 0.0114 0.752
DEMetro_Z_vs_SMC 3 -8.276 9.21e-07 -2.137
DEMetro_Z_vs_SMC 4 -6.979 6.46e-06 -1.802
DEMetro_Z_vs_SMC 5 3.743 0.00218 0.966
HMC_vs_DEMetro_Z 0 -13.954 1.32e-09 -3.603
HMC_vs_DEMetro_Z 1 -6.752 9.29e-06 -1.743
HMC_vs_DEMetro_Z 2 -7.973 1.42e-06 -2.059
HMC_vs_DEMetro_Z 3 -6.120 2.65e-05 -1.580
HMC_vs_DEMetro_Z 4 -5.753 5e-05 -1.485
HMC_vs_DEMetro_Z 5 -7.195 4.6e-06 -1.858
HMC_vs_Metro 0 -4.524 0.000477 -1.168
HMC_vs_Metro 1 -3.636 0.0027 -0.939
HMC_vs_Metro 2 -1.431 0.174 -0.370
HMC_vs_Metro 3 -4.302 0.00073 -1.111
HMC_vs_Metro 4 -4.347 0.00067 -1.122
HMC_vs_Metro 5 -5.418 9.06e-05 -1.399
HMC_vs_SMC 0 -20.921 5.84e-12 -5.402
HMC_vs_SMC 1 -28.116 1.02e-13 -7.259
HMC_vs_SMC 2 -25.840 3.26e-13 -6.672
HMC_vs_SMC 3 -22.382 2.33e-12 -5.779
HMC_vs_SMC 4 -57.349 5.16e-18 -14.807
HMC_vs_SMC 5 -29.028 6.57e-14 -7.495
Metro_vs_SMC 0 1.994 0.066 0.515
Metro_vs_SMC 1 2.581 0.0218 0.666
Metro_vs_SMC 2 0.317 0.756 0.082
Metro_vs_SMC 3 -14.716 6.55e-10 -3.800
Metro_vs_SMC 4 -15.391 3.62e-10 -3.974
Metro_vs_SMC 5 0.153 0.881 0.039
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.465 0.102 0.029 12.439
HMC 2.5 0.367 0.066 0.015 20.279
HMC 3.0 0.308 0.058 0.015 16.670
HMC 4.0 0.174 0.043 0.012 11.247
HMC 10.0 0.141 0.028 0.008 13.530
HMC 50.0 0.130 0.024 0.004 24.807
SMC 2.1 12.829 0.102 0.029 435.942
SMC 2.5 13.265 0.066 0.015 888.578
SMC 3.0 13.405 0.058 0.015 891.427
SMC 4.0 13.171 0.043 0.012 1122.116
SMC 10.0 8.648 0.028 0.008 1038.066
SMC 50.0 1.407 0.024 0.004 324.580
Metro 2.1 23.089 0.102 0.029 787.366
Metro 2.5 44.845 0.066 0.015 3014.570
Metro 3.0 17.146 0.058 0.015 1141.280
Metro 4.0 2.654 0.043 0.012 223.233
Metro 10.0 2.028 0.028 0.008 240.796
Metro 50.0 1.445 0.024 0.004 333.458
DEMetro_Z 2.1 30.764 0.102 0.029 1050.258
DEMetro_Z 2.5 60.489 0.066 0.015 4067.757
DEMetro_Z 3.0 21.453 0.058 0.015 1428.961
DEMetro_Z 4.0 4.236 0.043 0.012 358.437
DEMetro_Z 10.0 3.927 0.028 0.008 469.562
DEMetro_Z 50.0 2.872 0.024 0.004 668.479
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.138 0.000141 12.650
HMC 2.5 3.676 0.00249 34.905
HMC 3.0 6.742 7.55e-06 11.817
HMC 4.0 6.537 1.13e-05 13.430
HMC 10.0 6.329 1.49e-05 10.588
HMC 50.0 5.395 9e-05 16.598
SMC 2.1 41.199 2.42e-16 90.643
SMC 2.5 69.913 1.99e-19 214.440
SMC 3.0 75.746 6.21e-21 99.441
SMC 4.0 50.016 2.08e-17 140.012
SMC 10.0 101.613 1.13e-23 106.620
SMC 50.0 60.868 5.98e-19 111.073
Metro 2.1 15.646 2.84e-10 139.426
Metro 2.5 17.867 4.9e-11 327.845
Metro 3.0 9.368 2.07e-07 135.438
Metro 4.0 9.966 9.7e-08 153.981
Metro 10.0 7.487 2.93e-06 115.234
Metro 50.0 8.409 7.61e-07 164.802
DEMetro_Z 2.1 17.453 6.47e-11 120.199
DEMetro_Z 2.5 21.172 4.92e-12 354.487
DEMetro_Z 3.0 21.853 3.05e-12 145.521
DEMetro_Z 4.0 11.820 1.13e-08 187.387
DEMetro_Z 10.0 11.820 1.13e-08 146.467
DEMetro_Z 50.0 16.289 1.68e-10 231.589
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.113 0.00105 1.062
DEMetro_Z_vs_SMC 1 8.683 5.21e-07 2.242
DEMetro_Z_vs_SMC 2 6.794 8.69e-06 1.754
DEMetro_Z_vs_SMC 3 2.827 0.0134 0.730
DEMetro_Z_vs_SMC 4 3.125 0.00745 0.807
DEMetro_Z_vs_SMC 5 8.636 5.56e-07 2.230
HMC_vs_Metro 0 -13.568 1.91e-09 -3.503
HMC_vs_Metro 1 -14.234 1.02e-09 -3.675
HMC_vs_Metro 2 -8.751 4.75e-07 -2.260
HMC_vs_Metro 3 -8.799 4.45e-07 -2.272
HMC_vs_Metro 4 -6.624 1.14e-05 -1.710
HMC_vs_Metro 5 -8.480 6.91e-07 -2.189
Metro_vs_DEMetro_Z 0 1.617 0.128 0.418
Metro_vs_DEMetro_Z 1 -1.129 0.278 -0.291
Metro_vs_DEMetro_Z 2 -0.542 0.596 -0.140
Metro_vs_DEMetro_Z 3 -1.488 0.159 -0.384
Metro_vs_DEMetro_Z 4 -1.332 0.204 -0.344
Metro_vs_DEMetro_Z 5 -3.257 0.00573 -0.841
HMC_vs_SMC 0 -21.952 3.03e-12 -5.668
HMC_vs_SMC 1 -17.366 7.23e-11 -4.484
HMC_vs_SMC 2 -37.395 1.98e-15 -9.655
HMC_vs_SMC 3 -40.820 5.86e-16 -10.540
HMC_vs_SMC 4 -55.104 9e-18 -14.228
HMC_vs_SMC 5 -27.658 1.28e-13 -7.141
Metro_vs_SMC 0 5.206 0.000133 1.344
Metro_vs_SMC 1 6.156 2.5e-05 1.589
Metro_vs_SMC 2 2.490 0.026 0.643
Metro_vs_SMC 3 0.865 0.402 0.223
Metro_vs_SMC 4 0.554 0.589 0.143
Metro_vs_SMC 5 2.816 0.0137 0.727
HMC_vs_DEMetro_Z 0 -15.345 3.77e-10 -3.962
HMC_vs_DEMetro_Z 1 -14.914 5.49e-10 -3.851
HMC_vs_DEMetro_Z 2 -19.025 2.12e-11 -4.912
HMC_vs_DEMetro_Z 3 -10.910 3.14e-08 -2.817
HMC_vs_DEMetro_Z 4 -11.430 1.74e-08 -2.951
HMC_vs_DEMetro_Z 5 -15.829 2.49e-10 -4.087
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.090 0.016 0.006 12.650
HMC 2.5 0.105 0.015 0.003 34.905
HMC 3.0 0.082 0.015 0.006 11.817
HMC 4.0 0.069 0.014 0.004 13.430
HMC 10.0 0.074 0.014 0.006 10.588
HMC 50.0 0.077 0.015 0.004 16.598
SMC 2.1 0.547 0.016 0.006 90.643
SMC 2.5 0.572 0.015 0.003 214.440
SMC 3.0 0.575 0.015 0.006 99.441
SMC 4.0 0.597 0.014 0.004 140.012
SMC 10.0 0.616 0.014 0.006 106.620
SMC 50.0 0.433 0.015 0.004 111.073
Metro 2.1 0.833 0.016 0.006 139.426
Metro 2.5 0.866 0.015 0.003 327.845
Metro 3.0 0.777 0.015 0.006 135.438
Metro 4.0 0.655 0.014 0.004 153.981
Metro 10.0 0.664 0.014 0.006 115.234
Metro 50.0 0.635 0.015 0.004 164.802
DEMetro_Z 2.1 0.720 0.016 0.006 120.199
DEMetro_Z 2.5 0.936 0.015 0.003 354.487
DEMetro_Z 3.0 0.834 0.015 0.006 145.521
DEMetro_Z 4.0 0.795 0.014 0.004 187.387
DEMetro_Z 10.0 0.840 0.014 0.006 146.467
DEMetro_Z 50.0 0.887 0.015 0.004 231.589
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50

Vary_Tails_with_Dim_and_MM (Mixture, nu, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.805 0.0134 4.237
HMC 2.5 2.352 0.0337 8.966
HMC 3.0 2.584 0.0215 10.699
HMC 4.0 3.138 0.00719 11.339
HMC 10.0 5.582 5.99e-05 11.262
HMC 50.0 4.703 0.000337 36.223
SMC 2.1 31.465 7.31e-15 53.882
SMC 2.5 48.662 4.71e-17 346.209
SMC 3.0 21.625 2.93e-12 69.583
SMC 4.0 23.997 6.17e-13 63.858
SMC 10.0 22.758 5.11e-13 32.325
SMC 50.0 14.553 1.44e-10 15.262
Metro 2.1 2.700 0.0171 9.829
Metro 2.5 6.400 1.63e-05 39.892
Metro 3.0 3.665 0.00249 10.606
Metro 4.0 8.217 3.81e-07 8.083
Metro 10.0 7.467 9.73e-07 6.311
Metro 50.0 5.404 8.32e-05 11.044
DEMetro_Z 2.1 22.256 2.47e-12 261.930
DEMetro_Z 2.5 12.394 6.17e-09 1598.472
DEMetro_Z 3.0 30.372 3.43e-14 340.607
DEMetro_Z 4.0 23.439 1.23e-12 377.583
DEMetro_Z 10.0 20.409 7.96e-12 194.298
DEMetro_Z 50.0 9.883 1.08e-07 247.369
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -21.266 4.67e-12 -5.491
HMC_vs_DEMetro_Z 1 -12.247 7.2e-09 -3.162
HMC_vs_DEMetro_Z 2 -30.597 3.18e-14 -7.900
HMC_vs_DEMetro_Z 3 -23.207 1.42e-12 -5.992
HMC_vs_DEMetro_Z 4 -19.310 1.73e-11 -4.986
HMC_vs_DEMetro_Z 5 -9.388 2.03e-07 -2.424
Metro_vs_SMC 0 -9.700 1.36e-07 -2.505
Metro_vs_SMC 1 -39.115 1.06e-15 -10.099
Metro_vs_SMC 2 -10.894 3.2e-08 -2.813
Metro_vs_SMC 3 -21.625 3.72e-12 -5.584
Metro_vs_SMC 4 -15.003 5.08e-10 -3.874
Metro_vs_SMC 5 -1.934 0.0736 -0.499
Metro_vs_DEMetro_Z 0 -20.232 9.2e-12 -5.224
Metro_vs_DEMetro_Z 1 -11.950 9.87e-09 -3.085
Metro_vs_DEMetro_Z 2 -28.933 6.87e-14 -7.471
Metro_vs_DEMetro_Z 3 -23.487 1.21e-12 -6.064
Metro_vs_DEMetro_Z 4 -19.432 1.59e-11 -5.017
Metro_vs_DEMetro_Z 5 -9.527 1.7e-07 -2.460
HMC_vs_Metro 0 -1.345 0.2 -0.347
HMC_vs_Metro 1 -4.093 0.0011 -1.057
HMC_vs_Metro 2 0.017 0.987 0.004
HMC_vs_Metro 3 0.877 0.395 0.226
HMC_vs_Metro 4 2.085 0.0558 0.538
HMC_vs_Metro 5 3.280 0.00548 0.847
HMC_vs_SMC 0 -22.678 1.95e-12 -5.855
HMC_vs_SMC 1 -38.739 1.21e-15 -10.002
HMC_vs_SMC 2 -11.564 1.5e-08 -2.986
HMC_vs_SMC 3 -9.663 1.43e-07 -2.495
HMC_vs_SMC 4 -9.312 2.24e-07 -2.404
HMC_vs_SMC 5 2.871 0.0123 0.741
DEMetro_Z_vs_SMC 0 17.308 7.56e-11 4.469
DEMetro_Z_vs_SMC 1 9.636 1.48e-07 2.488
DEMetro_Z_vs_SMC 2 21.975 2.99e-12 5.674
DEMetro_Z_vs_SMC 3 19.864 1.18e-11 5.129
DEMetro_Z_vs_SMC 4 16.296 1.69e-10 4.208
DEMetro_Z_vs_SMC 5 9.303 2.27e-07 2.402
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.149 0.077 0.017 4.237
HMC 2.5 0.099 0.048 0.006 8.966
HMC 3.0 0.117 0.038 0.007 10.699
HMC 4.0 0.086 0.033 0.005 11.339
HMC 10.0 0.084 0.028 0.005 11.262
HMC 50.0 0.164 0.025 0.004 36.223
SMC 2.1 0.988 0.077 0.017 53.882
SMC 2.5 1.986 0.048 0.006 346.209
SMC 3.0 0.550 0.038 0.007 69.583
SMC 4.0 0.333 0.033 0.005 63.858
SMC 10.0 0.190 0.028 0.005 32.325
SMC 50.0 0.084 0.025 0.004 15.262
Metro 2.1 0.243 0.077 0.017 9.829
Metro 2.5 0.272 0.048 0.006 39.892
Metro 3.0 0.116 0.038 0.007 10.606
Metro 4.0 0.071 0.033 0.005 8.083
Metro 10.0 0.059 0.028 0.005 6.311
Metro 50.0 0.068 0.025 0.004 11.044
DEMetro_Z 2.1 4.507 0.077 0.017 261.930
DEMetro_Z 2.5 8.996 0.048 0.006 1598.472
DEMetro_Z 3.0 2.543 0.038 0.007 340.607
DEMetro_Z 4.0 1.809 0.033 0.005 377.583
DEMetro_Z 10.0 1.001 0.028 0.005 194.298
DEMetro_Z 50.0 0.974 0.025 0.004 247.369
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.224 0.237 0.954
HMC 2.5 1.428 0.174 1.978
HMC 3.0 1.427 0.168 0.784
HMC 4.0 1.710 0.102 0.934
HMC 10.0 3.511 0.00273 3.016
HMC 50.0 3.267 0.00556 12.732
SMC 2.1 135.093 2.83e-28 99.892
SMC 2.5 166.655 1.7e-24 3225.547
SMC 3.0 199.258 1.28e-25 1599.220
SMC 4.0 145.888 1.09e-23 2709.925
SMC 10.0 68.800 4.07e-19 6130.573
SMC 50.0 36.949 2.28e-15 423.550
Metro 2.1 1.365 0.189 0.961
Metro 2.5 2.451 0.0279 19.920
Metro 3.0 1.474 0.163 8.856
Metro 4.0 4.179 0.000501 2.696
Metro 10.0 7.552 6.66e-07 5.826
Metro 50.0 6.590 1.08e-06 3.348
DEMetro_Z 2.1 12.515 3.37e-09 22.471
DEMetro_Z 2.5 9.875 1.09e-07 1372.246
DEMetro_Z 3.0 24.345 7.26e-13 322.240
DEMetro_Z 4.0 15.378 3.65e-10 508.292
DEMetro_Z 10.0 9.757 1.27e-07 725.144
DEMetro_Z 50.0 5.009 0.000191 550.478
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -91.155 7.99e-21 -23.536
HMC_vs_SMC 1 -165.067 1.97e-24 -42.620
HMC_vs_SMC 2 -198.761 1.47e-25 -51.320
HMC_vs_SMC 3 -147.098 9.9e-24 -37.980
HMC_vs_SMC 4 -68.726 4.13e-19 -17.745
HMC_vs_SMC 5 -37.105 2.2e-15 -9.580
Metro_vs_DEMetro_Z 0 -10.273 6.68e-08 -2.652
Metro_vs_DEMetro_Z 1 -9.517 1.72e-07 -2.457
Metro_vs_DEMetro_Z 2 -21.545 3.91e-12 -5.563
Metro_vs_DEMetro_Z 3 -15.332 3.81e-10 -3.959
Metro_vs_DEMetro_Z 4 -9.675 1.4e-07 -2.498
Metro_vs_DEMetro_Z 5 -4.979 0.000202 -1.286
HMC_vs_Metro 0 -0.007 0.994 -0.002
HMC_vs_Metro 1 -2.142 0.0503 -0.553
HMC_vs_Metro 2 -1.327 0.206 -0.343
HMC_vs_Metro 3 -2.309 0.0367 -0.596
HMC_vs_Metro 4 -2.833 0.0133 -0.732
HMC_vs_Metro 5 2.325 0.0356 0.600
HMC_vs_DEMetro_Z 0 -10.849 3.37e-08 -2.801
HMC_vs_DEMetro_Z 1 -9.864 1.11e-07 -2.547
HMC_vs_DEMetro_Z 2 -24.310 7.52e-13 -6.277
HMC_vs_DEMetro_Z 3 -15.361 3.71e-10 -3.966
HMC_vs_DEMetro_Z 4 -9.725 1.32e-07 -2.511
HMC_vs_DEMetro_Z 5 -4.935 0.000219 -1.274
Metro_vs_SMC 0 -86.279 1.72e-20 -22.277
Metro_vs_SMC 1 -144.903 1.22e-23 -37.414
Metro_vs_SMC 2 -151.396 6.62e-24 -39.090
Metro_vs_SMC 3 -146.917 1.01e-23 -37.934
Metro_vs_SMC 4 -68.629 4.21e-19 -17.720
Metro_vs_SMC 5 -36.472 2.8e-15 -9.417
DEMetro_Z_vs_SMC 0 -42.288 3.59e-16 -10.919
DEMetro_Z_vs_SMC 1 -13.284 2.51e-09 -3.430
DEMetro_Z_vs_SMC 2 -78.670 6.26e-20 -20.312
DEMetro_Z_vs_SMC 3 -64.552 9.9e-19 -16.667
DEMetro_Z_vs_SMC 4 -40.797 5.91e-16 -10.534
DEMetro_Z_vs_SMC 5 1.160 0.265 0.300
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 24.898 13.186 12.273 0.954
HMC 2.5 2.844 1.243 0.809 1.978
HMC 3.0 0.754 0.540 0.272 0.784
HMC 4.0 0.268 0.193 0.080 0.934
HMC 10.0 0.102 0.060 0.014 3.016
HMC 50.0 0.221 0.040 0.014 12.732
SMC 2.1 1239.191 13.186 12.273 99.892
SMC 2.5 2611.265 1.243 0.809 3225.547
SMC 3.0 436.041 0.540 0.272 1599.220
SMC 4.0 217.386 0.193 0.080 2709.925
SMC 10.0 86.451 0.060 0.014 6130.573
SMC 50.0 6.066 0.040 0.014 423.550
Metro 2.1 24.980 13.186 12.273 0.961
Metro 2.5 17.362 1.243 0.809 19.920
Metro 3.0 2.952 0.540 0.272 8.856
Metro 4.0 0.409 0.193 0.080 2.696
Metro 10.0 0.142 0.060 0.014 5.826
Metro 50.0 0.087 0.040 0.014 3.348
DEMetro_Z 2.1 288.983 13.186 12.273 22.471
DEMetro_Z 2.5 1111.626 1.243 0.809 1372.246
DEMetro_Z 3.0 88.293 0.540 0.272 322.240
DEMetro_Z 4.0 40.931 0.193 0.080 508.292
DEMetro_Z 10.0 10.278 0.060 0.014 725.144
DEMetro_Z 50.0 7.871 0.040 0.014 550.478
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.279 0.00544 14.640
HMC 2.5 5.285 0.000108 13.998
HMC 3.0 3.017 0.00914 10.994
HMC 4.0 2.461 0.0274 19.070
HMC 10.0 5.713 4.98e-05 15.033
HMC 50.0 4.631 0.000388 47.708
SMC 2.1 275.920 1.03e-27 1217.376
SMC 2.5 337.158 8.8e-29 6244.711
SMC 3.0 348.242 4.18e-29 1718.637
SMC 4.0 273.460 1.62e-27 3718.140
SMC 10.0 114.873 3.1e-22 2247.916
SMC 50.0 48.148 5.71e-17 530.166
Metro 2.1 3.739 0.0022 32.435
Metro 2.5 4.120 0.00104 188.842
Metro 3.0 2.117 0.0527 28.168
Metro 4.0 8.927 3.05e-07 20.101
Metro 10.0 10.740 9.86e-09 10.626
Metro 50.0 5.329 0.0001 14.965
DEMetro_Z 2.1 28.911 6.89e-14 533.953
DEMetro_Z 2.5 20.084 1.02e-11 3890.352
DEMetro_Z 3.0 56.035 6.93e-18 675.585
DEMetro_Z 4.0 26.811 1.96e-13 1324.667
DEMetro_Z 10.0 21.218 4.8e-12 577.352
DEMetro_Z 50.0 11.816 1.14e-08 527.589
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -24.181 8.09e-13 -6.243
Metro_vs_DEMetro_Z 1 -17.397 7.06e-11 -4.492
Metro_vs_DEMetro_Z 2 -35.717 3.74e-15 -9.222
Metro_vs_DEMetro_Z 3 -26.330 2.52e-13 -6.798
Metro_vs_DEMetro_Z 4 -20.702 6.73e-12 -5.345
Metro_vs_DEMetro_Z 5 -11.594 1.45e-08 -2.994
DEMetro_Z_vs_SMC 0 -34.448 6.17e-15 -8.895
DEMetro_Z_vs_SMC 1 -11.999 9.36e-09 -3.098
DEMetro_Z_vs_SMC 2 -78.526 6.42e-20 -20.275
DEMetro_Z_vs_SMC 3 -49.147 4.43e-17 -12.690
DEMetro_Z_vs_SMC 4 -43.421 2.48e-16 -11.211
DEMetro_Z_vs_SMC 5 -0.057 0.955 -0.015
HMC_vs_DEMetro_Z 0 -29.035 6.55e-14 -7.497
HMC_vs_DEMetro_Z 1 -20.014 1.07e-11 -5.168
HMC_vs_DEMetro_Z 2 -52.398 1.82e-17 -13.529
HMC_vs_DEMetro_Z 3 -26.656 2.13e-13 -6.882
HMC_vs_DEMetro_Z 4 -20.096 1.01e-11 -5.189
HMC_vs_DEMetro_Z 5 -11.471 1.67e-08 -2.962
HMC_vs_Metro 0 -1.857 0.0845 -0.479
HMC_vs_Metro 1 -3.763 0.0021 -0.972
HMC_vs_Metro 2 -1.218 0.244 -0.314
HMC_vs_Metro 3 -0.123 0.904 -0.032
HMC_vs_Metro 4 1.577 0.137 0.407
HMC_vs_Metro 5 3.164 0.0069 0.817
HMC_vs_SMC 0 -197.747 1.58e-25 -51.058
HMC_vs_SMC 1 -332.067 1.11e-28 -85.739
HMC_vs_SMC 2 -309.264 3.01e-28 -79.852
HMC_vs_SMC 3 -244.995 7.86e-27 -63.257
HMC_vs_SMC 4 -113.503 3.72e-22 -29.306
HMC_vs_SMC 5 -34.849 5.26e-15 -8.998
Metro_vs_SMC 0 -109.378 6.25e-22 -28.241
Metro_vs_SMC 1 -118.664 2e-22 -30.639
Metro_vs_SMC 2 -116.031 2.74e-22 -29.959
Metro_vs_SMC 3 -267.896 2.25e-27 -69.170
Metro_vs_SMC 4 -112.613 4.16e-22 -29.077
Metro_vs_SMC 5 -42.785 3.05e-16 -11.047
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.449 0.131 0.022 14.640
HMC 2.5 0.170 0.084 0.006 13.998
HMC 3.0 0.165 0.067 0.009 10.994
HMC 4.0 0.106 0.052 0.003 19.070
HMC 10.0 0.080 0.038 0.003 15.033
HMC 50.0 0.139 0.033 0.002 47.708
SMC 2.1 26.631 0.131 0.022 1217.376
SMC 2.5 38.579 0.084 0.006 6244.711
SMC 3.0 15.403 0.067 0.009 1718.637
SMC 4.0 10.629 0.052 0.003 3718.140
SMC 10.0 6.440 0.038 0.003 2247.916
SMC 50.0 1.204 0.033 0.002 530.166
Metro 2.1 0.837 0.131 0.022 32.435
Metro 2.5 1.248 0.084 0.006 188.842
Metro 3.0 0.319 0.067 0.009 28.168
Metro 4.0 0.109 0.052 0.003 20.101
Metro 10.0 0.068 0.038 0.003 10.626
Metro 50.0 0.066 0.033 0.002 14.965
DEMetro_Z 2.1 11.754 0.131 0.022 533.953
DEMetro_Z 2.5 24.065 0.084 0.006 3890.352
DEMetro_Z 3.0 6.096 0.067 0.009 675.585
DEMetro_Z 4.0 3.820 0.052 0.003 1324.667
DEMetro_Z 10.0 1.682 0.038 0.003 577.352
DEMetro_Z 50.0 1.198 0.033 0.002 527.589
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.140 0.000993 25.037
HMC 2.5 3.445 0.0039 14.602
HMC 3.0 2.960 0.0103 15.157
HMC 4.0 2.770 0.015 13.839
HMC 10.0 5.655 5.29e-05 11.875
HMC 50.0 4.746 0.000311 41.645
SMC 2.1 126.626 9.89e-24 210.879
SMC 2.5 161.240 5.54e-26 205.964
SMC 3.0 111.181 2.99e-23 157.115
SMC 4.0 127.499 1.12e-23 224.508
SMC 10.0 125.783 7.21e-24 191.785
SMC 50.0 92.477 1.55e-21 175.803
Metro 2.1 4.818 0.000272 48.192
Metro 2.5 7.392 3.38e-06 93.408
Metro 3.0 3.265 0.00562 22.366
Metro 4.0 9.318 1.28e-07 13.145
Metro 10.0 10.002 9.49e-09 7.336
Metro 50.0 5.557 6.46e-05 12.990
DEMetro_Z 2.1 50.749 2.39e-17 245.456
DEMetro_Z 2.5 58.441 3.08e-18 240.291
DEMetro_Z 3.0 64.153 6.17e-19 181.414
DEMetro_Z 4.0 63.577 9.22e-19 251.543
DEMetro_Z 10.0 49.823 2.72e-17 181.926
DEMetro_Z 50.0 26.809 1.88e-13 220.536
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.656 1.09e-05 1.719
DEMetro_Z_vs_SMC 1 7.799 1.84e-06 2.014
DEMetro_Z_vs_SMC 2 8.083 1.21e-06 2.087
DEMetro_Z_vs_SMC 3 6.157 2.49e-05 1.590
DEMetro_Z_vs_SMC 4 -2.512 0.0249 -0.649
DEMetro_Z_vs_SMC 5 5.709 5.4e-05 1.474
HMC_vs_Metro 0 -3.119 0.00754 -0.805
HMC_vs_Metro 1 -5.754 4.99e-05 -1.486
HMC_vs_Metro 2 -0.787 0.444 -0.203
HMC_vs_Metro 3 0.127 0.901 0.033
HMC_vs_Metro 4 1.984 0.0673 0.512
HMC_vs_Metro 5 3.304 0.00522 0.853
Metro_vs_DEMetro_Z 0 -17.323 7.47e-11 -4.473
Metro_vs_DEMetro_Z 1 -9.837 1.14e-07 -2.540
Metro_vs_DEMetro_Z 2 -21.156 5.01e-12 -5.463
Metro_vs_DEMetro_Z 3 -54.741 9.87e-18 -14.134
Metro_vs_DEMetro_Z 4 -46.626 9.22e-17 -12.039
Metro_vs_DEMetro_Z 5 -25.901 3.15e-13 -6.688
HMC_vs_SMC 0 -31.483 2.14e-14 -8.129
HMC_vs_SMC 1 -38.364 1.39e-15 -9.906
HMC_vs_SMC 2 -27.512 1.38e-13 -7.104
HMC_vs_SMC 3 -38.075 1.54e-15 -9.831
HMC_vs_SMC 4 -92.666 6.35e-21 -23.926
HMC_vs_SMC 5 -15.229 4.17e-10 -3.932
Metro_vs_SMC 0 -16.194 1.84e-10 -4.181
Metro_vs_SMC 1 -9.030 3.26e-07 -2.331
Metro_vs_SMC 2 -18.694 2.68e-11 -4.827
Metro_vs_SMC 3 -98.552 2.68e-21 -25.446
Metro_vs_SMC 4 -101.702 1.73e-21 -26.259
Metro_vs_SMC 5 -49.208 4.36e-17 -12.705
HMC_vs_DEMetro_Z 0 -31.771 1.89e-14 -8.203
HMC_vs_DEMetro_Z 1 -45.738 1.21e-16 -11.809
HMC_vs_DEMetro_Z 2 -30.832 2.86e-14 -7.961
HMC_vs_DEMetro_Z 3 -40.410 6.74e-16 -10.434
HMC_vs_DEMetro_Z 4 -38.725 1.22e-15 -9.999
HMC_vs_DEMetro_Z 5 -18.879 2.35e-11 -4.874
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.062 0.015 0.002 25.037
HMC 2.5 0.043 0.014 0.002 14.602
HMC 3.0 0.052 0.014 0.002 15.157
HMC 4.0 0.038 0.014 0.002 13.839
HMC 10.0 0.037 0.013 0.002 11.875
HMC 50.0 0.074 0.013 0.001 41.645
SMC 2.1 0.412 0.015 0.002 210.879
SMC 2.5 0.413 0.014 0.002 205.964
SMC 3.0 0.405 0.014 0.002 157.115
SMC 4.0 0.401 0.014 0.002 224.508
SMC 10.0 0.396 0.013 0.002 191.785
SMC 50.0 0.271 0.013 0.001 175.803
Metro 2.1 0.106 0.015 0.002 48.192
Metro 2.5 0.195 0.014 0.002 93.408
Metro 3.0 0.070 0.014 0.002 22.366
Metro 4.0 0.037 0.014 0.002 13.145
Metro 10.0 0.028 0.013 0.002 7.336
Metro 50.0 0.032 0.013 0.001 12.990
DEMetro_Z 2.1 0.477 0.015 0.002 245.456
DEMetro_Z 2.5 0.480 0.014 0.002 240.291
DEMetro_Z 3.0 0.466 0.014 0.002 181.414
DEMetro_Z 4.0 0.447 0.014 0.002 251.543
DEMetro_Z 10.0 0.376 0.013 0.002 181.926
DEMetro_Z 50.0 0.337 0.013 0.001 220.536
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.331 0.204 3.113
HMC 2.5 4.416 0.000552 9.910
HMC 3.0 3.981 0.00128 7.907
HMC 4.0 3.753 0.00204 7.749
HMC 10.0 5.366 9.5e-05 16.735
HMC 50.0 4.420 0.000582 77.911
SMC 2.1 27.399 5.66e-14 48.203
SMC 2.5 41.633 4.18e-16 311.696
SMC 3.0 22.224 1.98e-12 69.346
SMC 4.0 25.726 2.1e-13 60.828
SMC 10.0 28.968 4.76e-15 31.272
SMC 50.0 13.044 9.46e-10 15.144
Metro 2.1 4.832 0.000168 4.311
Metro 2.5 3.992 0.00133 39.816
Metro 3.0 8.074 4.17e-07 7.414
Metro 4.0 8.925 1.55e-07 9.716
Metro 10.0 9.288 1.85e-08 6.173
Metro 50.0 3.565 0.00308 15.545
DEMetro_Z 2.1 12.238 7.24e-09 230.329
DEMetro_Z 2.5 12.215 7.45e-09 1537.982
DEMetro_Z 3.0 16.282 1.7e-10 350.495
DEMetro_Z 4.0 17.352 7.26e-11 345.661
DEMetro_Z 10.0 13.675 1.71e-09 207.852
DEMetro_Z 50.0 13.152 2.85e-09 250.949
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -12.391 6.19e-09 -3.199
HMC_vs_DEMetro_Z 1 -12.060 8.78e-09 -3.114
HMC_vs_DEMetro_Z 2 -16.195 1.84e-10 -4.181
HMC_vs_DEMetro_Z 3 -16.631 1.29e-10 -4.294
HMC_vs_DEMetro_Z 4 -13.121 2.95e-09 -3.388
HMC_vs_DEMetro_Z 5 -6.221 2.23e-05 -1.606
Metro_vs_SMC 0 -21.772 3.39e-12 -5.622
Metro_vs_SMC 1 -18.586 2.9e-11 -4.799
Metro_vs_SMC 2 -17.280 7.72e-11 -4.462
Metro_vs_SMC 3 -20.309 8.74e-12 -5.244
Metro_vs_SMC 4 -19.707 1.31e-11 -5.088
Metro_vs_SMC 5 0.090 0.93 0.023
Metro_vs_DEMetro_Z 0 -11.945 9.92e-09 -3.084
Metro_vs_DEMetro_Z 1 -11.839 1.11e-08 -3.057
Metro_vs_DEMetro_Z 2 -16.270 1.73e-10 -4.201
Metro_vs_DEMetro_Z 3 -16.926 1.02e-10 -4.370
Metro_vs_DEMetro_Z 4 -13.090 3.04e-09 -3.380
Metro_vs_DEMetro_Z 5 -14.244 1.01e-09 -3.678
HMC_vs_Metro 0 -0.480 0.639 -0.124
HMC_vs_Metro 1 -3.298 0.00528 -0.852
HMC_vs_Metro 2 0.258 0.8 0.067
HMC_vs_Metro 3 -0.779 0.449 -0.201
HMC_vs_Metro 4 3.186 0.0066 0.823
HMC_vs_Metro 5 3.162 0.00693 0.816
HMC_vs_SMC 0 -15.269 4.02e-10 -3.943
HMC_vs_SMC 1 -34.431 6.21e-15 -8.890
HMC_vs_SMC 2 -19.376 1.65e-11 -5.003
HMC_vs_SMC 3 -18.013 4.42e-11 -4.651
HMC_vs_SMC 4 -4.407 0.000597 -1.138
HMC_vs_SMC 5 3.553 0.00318 0.917
DEMetro_Z_vs_SMC 0 9.918 1.03e-07 2.561
DEMetro_Z_vs_SMC 1 9.732 1.31e-07 2.513
DEMetro_Z_vs_SMC 2 12.868 3.8e-09 3.323
DEMetro_Z_vs_SMC 3 14.193 1.06e-09 3.665
DEMetro_Z_vs_SMC 4 11.396 1.81e-08 2.942
DEMetro_Z_vs_SMC 5 12.300 6.81e-09 3.176
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.130 0.077 0.017 3.113
HMC 2.5 0.104 0.048 0.006 9.910
HMC 3.0 0.097 0.038 0.007 7.907
HMC 4.0 0.070 0.033 0.005 7.749
HMC 10.0 0.112 0.028 0.005 16.735
HMC 50.0 0.324 0.025 0.004 77.911
SMC 2.1 0.892 0.077 0.017 48.203
SMC 2.5 1.793 0.048 0.006 311.696
SMC 3.0 0.548 0.038 0.007 69.346
SMC 4.0 0.319 0.033 0.005 60.828
SMC 10.0 0.185 0.028 0.005 31.272
SMC 50.0 0.083 0.025 0.004 15.144
Metro 2.1 0.150 0.077 0.017 4.311
Metro 2.5 0.271 0.048 0.006 39.816
Metro 3.0 0.093 0.038 0.007 7.414
Metro 4.0 0.079 0.033 0.005 9.716
Metro 10.0 0.059 0.028 0.005 6.173
Metro 50.0 0.085 0.025 0.004 15.545
DEMetro_Z 2.1 3.972 0.077 0.017 230.329
DEMetro_Z 2.5 8.657 0.048 0.006 1537.982
DEMetro_Z 3.0 2.616 0.038 0.007 350.495
DEMetro_Z 4.0 1.659 0.033 0.005 345.661
DEMetro_Z 10.0 1.069 0.028 0.005 207.852
DEMetro_Z 50.0 0.988 0.025 0.004 250.949
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.815 0.425 0.530
HMC 2.5 1.415 0.179 11.671
HMC 3.0 1.734 0.102 1.738
HMC 4.0 0.390 0.699 0.139
HMC 10.0 4.133 0.000829 4.701
HMC 50.0 3.055 0.00856 64.116
SMC 2.1 141.375 1.69e-29 97.195
SMC 2.5 154.332 4.98e-24 3058.491
SMC 3.0 176.142 7.33e-25 1544.614
SMC 4.0 130.591 5.16e-23 2660.405
SMC 10.0 56.886 5.77e-18 5634.330
SMC 50.0 51.918 1.88e-17 341.220
Metro 2.1 0.151 0.881 0.088
Metro 2.5 1.429 0.175 36.645
Metro 3.0 3.247 0.00379 1.776
Metro 4.0 3.155 0.00653 4.332
Metro 10.0 6.842 2.24e-06 5.073
Metro 50.0 2.606 0.0204 5.797
DEMetro_Z 2.1 6.157 1.98e-05 9.934
DEMetro_Z 2.5 6.044 3.02e-05 734.831
DEMetro_Z 3.0 7.403 3.33e-06 153.667
DEMetro_Z 4.0 7.511 2.83e-06 191.202
DEMetro_Z 10.0 6.889 7.45e-06 303.921
DEMetro_Z 50.0 4.059 0.00117 305.226
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -84.977 2.13e-20 -21.941
HMC_vs_SMC 1 -161.268 2.73e-24 -41.639
HMC_vs_SMC 2 -178.830 6.44e-25 -46.174
HMC_vs_SMC 3 -130.967 5.03e-23 -33.816
HMC_vs_SMC 4 -56.858 5.82e-18 -14.681
HMC_vs_SMC 5 -12.327 6.62e-09 -3.183
Metro_vs_DEMetro_Z 0 -5.914 3.77e-05 -1.527
Metro_vs_DEMetro_Z 1 -5.648 6.01e-05 -1.458
Metro_vs_DEMetro_Z 2 -7.304 3.89e-06 -1.886
Metro_vs_DEMetro_Z 3 -7.164 4.83e-06 -1.850
Metro_vs_DEMetro_Z 4 -6.756 9.23e-06 -1.744
Metro_vs_DEMetro_Z 5 -4.086 0.00111 -1.055
HMC_vs_Metro 0 1.176 0.259 0.304
HMC_vs_Metro 1 -0.895 0.386 -0.231
HMC_vs_Metro 2 -0.034 0.974 -0.009
HMC_vs_Metro 3 -2.901 0.0116 -0.749
HMC_vs_Metro 4 -0.261 0.798 -0.067
HMC_vs_Metro 5 2.746 0.0158 0.709
HMC_vs_DEMetro_Z 0 -5.807 4.55e-05 -1.499
HMC_vs_DEMetro_Z 1 -5.889 3.94e-05 -1.521
HMC_vs_DEMetro_Z 2 -7.278 4.04e-06 -1.879
HMC_vs_DEMetro_Z 3 -7.518 2.8e-06 -1.941
HMC_vs_DEMetro_Z 4 -6.754 9.27e-06 -1.744
HMC_vs_DEMetro_Z 5 -2.918 0.0112 -0.753
Metro_vs_SMC 0 -94.525 4.81e-21 -24.406
Metro_vs_SMC 1 -84.338 2.37e-20 -21.776
Metro_vs_SMC 2 -179.435 6.14e-25 -46.330
Metro_vs_SMC 3 -132.588 4.23e-23 -34.234
Metro_vs_SMC 4 -56.808 5.89e-18 -14.668
Metro_vs_SMC 5 -52.364 1.83e-17 -13.520
DEMetro_Z_vs_SMC 0 -57.319 5.2e-18 -14.800
DEMetro_Z_vs_SMC 1 -19.758 1.27e-11 -5.102
DEMetro_Z_vs_SMC 2 -59.120 3.38e-18 -15.265
DEMetro_Z_vs_SMC 3 -70.449 2.92e-19 -18.190
DEMetro_Z_vs_SMC 4 -50.453 3.08e-17 -13.027
DEMetro_Z_vs_SMC 5 -0.488 0.633 -0.126
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 19.696 13.186 12.273 0.530
HMC 2.5 10.687 1.243 0.809 11.671
HMC 3.0 1.014 0.540 0.272 1.738
HMC 4.0 0.204 0.193 0.080 0.139
HMC 10.0 0.126 0.060 0.014 4.701
HMC 50.0 0.952 0.040 0.014 64.116
SMC 2.1 1206.086 13.186 12.273 97.195
SMC 2.5 2476.088 1.243 0.809 3058.491
SMC 3.0 421.171 0.540 0.272 1544.614
SMC 4.0 213.417 0.193 0.080 2660.405
SMC 10.0 79.458 0.060 0.014 5634.330
SMC 50.0 4.894 0.040 0.014 341.220
Metro 2.1 14.267 13.186 12.273 0.088
Metro 2.5 30.896 1.243 0.809 36.645
Metro 3.0 1.024 0.540 0.272 1.776
Metro 4.0 0.540 0.193 0.080 4.332
Metro 10.0 0.131 0.060 0.014 5.073
Metro 50.0 0.122 0.040 0.014 5.797
DEMetro_Z 2.1 135.109 13.186 12.273 9.934
DEMetro_Z 2.5 595.848 1.243 0.809 734.831
DEMetro_Z 3.0 42.387 0.540 0.272 153.667
DEMetro_Z 4.0 15.517 0.193 0.080 191.202
DEMetro_Z 10.0 4.342 0.060 0.014 303.921
DEMetro_Z 50.0 4.382 0.040 0.014 305.226
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.565 0.14 19.428
HMC 2.5 2.399 0.0309 36.424
HMC 3.0 5.799 3.9e-05 10.281
HMC 4.0 4.476 0.000494 10.749
HMC 10.0 5.571 6.69e-05 22.229
HMC 50.0 4.356 0.000658 104.282
SMC 2.1 378.939 8.05e-30 1199.821
SMC 2.5 308.542 3.05e-28 6079.522
SMC 3.0 322.762 1.26e-28 1685.795
SMC 4.0 220.494 3.35e-26 3678.199
SMC 10.0 91.975 6.98e-21 2140.719
SMC 50.0 65.035 8.14e-19 455.054
Metro 2.1 6.052 2.62e-05 12.816
Metro 2.5 1.642 0.123 184.147
Metro 3.0 7.075 4.4e-06 12.633
Metro 4.0 6.466 1.43e-05 26.228
Metro 10.0 10.956 6.2e-09 10.207
Metro 50.0 3.685 0.00243 20.066
DEMetro_Z 2.1 11.620 1.41e-08 337.882
DEMetro_Z 2.5 11.987 9.48e-09 2645.330
DEMetro_Z 3.0 13.780 1.55e-09 445.022
DEMetro_Z 4.0 14.507 7.91e-10 791.321
DEMetro_Z 10.0 13.787 1.54e-09 382.839
DEMetro_Z 50.0 10.753 3.77e-08 388.989
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -11.291 2.04e-08 -2.915
Metro_vs_DEMetro_Z 1 -10.652 4.25e-08 -2.750
Metro_vs_DEMetro_Z 2 -13.261 2.57e-09 -3.424
Metro_vs_DEMetro_Z 3 -13.732 1.63e-09 -3.546
Metro_vs_DEMetro_Z 4 -13.309 2.45e-09 -3.436
Metro_vs_DEMetro_Z 5 -11.357 1.89e-08 -2.932
DEMetro_Z_vs_SMC 0 -30.913 2.76e-14 -7.982
DEMetro_Z_vs_SMC 1 -15.694 2.79e-10 -4.052
DEMetro_Z_vs_SMC 2 -37.025 2.27e-15 -9.560
DEMetro_Z_vs_SMC 3 -48.850 4.82e-17 -12.613
DEMetro_Z_vs_SMC 4 -56.796 5.91e-18 -14.665
DEMetro_Z_vs_SMC 5 -1.787 0.0956 -0.461
HMC_vs_DEMetro_Z 0 -10.448 5.42e-08 -2.698
HMC_vs_DEMetro_Z 1 -11.863 1.08e-08 -3.063
HMC_vs_DEMetro_Z 2 -13.314 2.44e-09 -3.438
HMC_vs_DEMetro_Z 3 -14.264 9.88e-10 -3.683
HMC_vs_DEMetro_Z 4 -13.090 3.04e-09 -3.380
HMC_vs_DEMetro_Z 5 -5.984 3.34e-05 -1.545
HMC_vs_Metro 0 0.507 0.62 0.131
HMC_vs_Metro 1 -1.290 0.218 -0.333
HMC_vs_Metro 2 -1.068 0.303 -0.276
HMC_vs_Metro 3 -3.044 0.00875 -0.786
HMC_vs_Metro 4 2.864 0.0125 0.739
HMC_vs_Metro 5 3.171 0.0068 0.819
HMC_vs_SMC 0 -82.523 3.21e-20 -21.307
HMC_vs_SMC 1 -302.382 4.13e-28 -78.075
HMC_vs_SMC 2 -311.789 2.69e-28 -80.503
HMC_vs_SMC 3 -218.979 3.78e-26 -56.540
HMC_vs_SMC 4 -89.381 1.05e-20 -23.078
HMC_vs_SMC 5 -13.218 2.68e-09 -3.413
Metro_vs_SMC 0 -330.918 1.17e-28 -85.443
Metro_vs_SMC 1 -49.278 4.27e-17 -12.724
Metro_vs_SMC 2 -358.008 3.88e-29 -92.437
Metro_vs_SMC 3 -223.521 2.84e-26 -57.713
Metro_vs_SMC 4 -92.246 6.76e-21 -23.818
Metro_vs_SMC 5 -61.698 1.86e-18 -15.930
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.554 0.131 0.022 19.428
HMC 2.5 0.308 0.084 0.006 36.424
HMC 3.0 0.159 0.067 0.009 10.281
HMC 4.0 0.083 0.052 0.003 10.749
HMC 10.0 0.101 0.038 0.003 22.229
HMC 50.0 0.264 0.033 0.002 104.282
SMC 2.1 26.249 0.131 0.022 1199.821
SMC 2.5 37.560 0.084 0.006 6079.522
SMC 3.0 15.110 0.067 0.009 1685.795
SMC 4.0 10.516 0.052 0.003 3678.199
SMC 10.0 6.135 0.038 0.003 2140.719
SMC 50.0 1.038 0.033 0.002 455.054
Metro 2.1 0.410 0.131 0.022 12.816
Metro 2.5 1.219 0.084 0.006 184.147
Metro 3.0 0.180 0.067 0.009 12.633
Metro 4.0 0.127 0.052 0.003 26.228
Metro 10.0 0.067 0.038 0.003 10.207
Metro 50.0 0.078 0.033 0.002 20.066
DEMetro_Z 2.1 7.486 0.131 0.022 337.882
DEMetro_Z 2.5 16.391 0.084 0.006 2645.330
DEMetro_Z 3.0 4.038 0.067 0.009 445.022
DEMetro_Z 4.0 2.303 0.052 0.003 791.321
DEMetro_Z 10.0 1.128 0.038 0.003 382.839
DEMetro_Z 50.0 0.892 0.033 0.002 388.989
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.212 0.0441 27.521
HMC 2.5 3.498 0.00352 17.490
HMC 3.0 6.272 1.79e-05 13.322
HMC 4.0 4.389 0.000577 9.252
HMC 10.0 5.377 9.35e-05 17.582
HMC 50.0 4.310 0.000719 91.228
SMC 2.1 154.246 1.89e-25 212.407
SMC 2.5 174.176 9.36e-27 207.771
SMC 3.0 134.901 4.5e-25 159.954
SMC 4.0 198.311 9.12e-28 228.966
SMC 10.0 218.608 3.44e-30 192.053
SMC 50.0 92.361 1.18e-21 160.233
Metro 2.1 6.310 1.88e-05 35.163
Metro 2.5 4.363 0.000648 56.613
Metro 3.0 6.793 7.44e-06 14.321
Metro 4.0 9.429 1.28e-07 15.569
Metro 10.0 9.682 1.7e-08 7.244
Metro 50.0 3.646 0.00263 18.169
DEMetro_Z 2.1 36.244 2.85e-15 254.164
DEMetro_Z 2.5 45.619 1.12e-16 271.999
DEMetro_Z 3.0 41.611 3.75e-16 187.121
DEMetro_Z 4.0 30.152 3.72e-14 249.659
DEMetro_Z 10.0 19.116 1.94e-11 185.690
DEMetro_Z 50.0 39.604 8.14e-16 246.980
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.477 8.16e-05 1.414
DEMetro_Z_vs_SMC 1 11.262 2.1e-08 2.908
DEMetro_Z_vs_SMC 2 6.185 2.37e-05 1.597
DEMetro_Z_vs_SMC 3 2.509 0.025 0.648
DEMetro_Z_vs_SMC 4 -0.628 0.54 -0.162
DEMetro_Z_vs_SMC 5 12.908 3.65e-09 3.333
HMC_vs_Metro 0 -0.509 0.619 -0.131
HMC_vs_Metro 1 -2.890 0.0119 -0.746
HMC_vs_Metro 2 -0.352 0.73 -0.091
HMC_vs_Metro 3 -2.161 0.0485 -0.558
HMC_vs_Metro 4 2.929 0.011 0.756
HMC_vs_Metro 5 3.118 0.00755 0.805
Metro_vs_DEMetro_Z 0 -24.733 5.94e-13 -6.386
Metro_vs_DEMetro_Z 1 -16.187 1.85e-10 -4.180
Metro_vs_DEMetro_Z 2 -34.348 6.42e-15 -8.869
Metro_vs_DEMetro_Z 3 -29.700 4.79e-14 -7.668
Metro_vs_DEMetro_Z 4 -18.292 3.59e-11 -4.723
Metro_vs_DEMetro_Z 5 -31.315 2.31e-14 -8.086
HMC_vs_SMC 0 -14.466 8.21e-10 -3.735
HMC_vs_SMC 1 -38.545 1.3e-15 -9.952
HMC_vs_SMC 2 -66.749 6.21e-19 -17.235
HMC_vs_SMC 3 -86.179 1.75e-20 -22.251
HMC_vs_SMC 4 -50.392 3.13e-17 -13.011
HMC_vs_SMC 5 -3.276 0.00552 -0.846
Metro_vs_SMC 0 -32.767 1.23e-14 -8.460
Metro_vs_SMC 1 -12.169 7.82e-09 -3.142
Metro_vs_SMC 2 -52.610 1.72e-17 -13.584
Metro_vs_SMC 3 -116.489 2.59e-22 -30.077
Metro_vs_SMC 4 -199.651 1.38e-25 -51.550
Metro_vs_SMC 5 -26.927 1.85e-13 -6.952
HMC_vs_DEMetro_Z 0 -16.705 1.22e-10 -4.313
HMC_vs_DEMetro_Z 1 -33.743 8.21e-15 -8.712
HMC_vs_DEMetro_Z 2 -44.649 1.69e-16 -11.528
HMC_vs_DEMetro_Z 3 -27.190 1.62e-13 -7.020
HMC_vs_DEMetro_Z 4 -18.746 2.58e-11 -4.840
HMC_vs_DEMetro_Z 5 -7.303 3.89e-06 -1.886
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.067 0.015 0.002 27.521
HMC 2.5 0.048 0.014 0.002 17.490
HMC 3.0 0.048 0.014 0.002 13.322
HMC 4.0 0.030 0.014 0.002 9.252
HMC 10.0 0.048 0.013 0.002 17.582
HMC 50.0 0.147 0.013 0.001 91.228
SMC 2.1 0.415 0.015 0.002 212.407
SMC 2.5 0.417 0.014 0.002 207.771
SMC 3.0 0.412 0.014 0.002 159.954
SMC 4.0 0.408 0.014 0.002 228.966
SMC 10.0 0.396 0.013 0.002 192.053
SMC 50.0 0.248 0.013 0.001 160.233
Metro 2.1 0.082 0.015 0.002 35.163
Metro 2.5 0.124 0.014 0.002 56.613
Metro 3.0 0.050 0.014 0.002 14.321
Metro 4.0 0.041 0.014 0.002 15.569
Metro 10.0 0.028 0.013 0.002 7.244
Metro 50.0 0.040 0.013 0.001 18.169
DEMetro_Z 2.1 0.494 0.015 0.002 254.164
DEMetro_Z 2.5 0.541 0.014 0.002 271.999
DEMetro_Z 3.0 0.480 0.014 0.002 187.121
DEMetro_Z 4.0 0.444 0.014 0.002 249.659
DEMetro_Z 10.0 0.384 0.013 0.002 185.690
DEMetro_Z 50.0 0.375 0.013 0.001 246.980
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50

Vary_Tails_with_Corr_and_MM (Mixture, nu, 15 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.294 0.0327 1.367
HMC 2.5 4.758 0.000197 4.264
HMC 3.0 4.937 0.000133 4.315
HMC 4.0 5.938 2.04e-05 5.812
HMC 10.0 4.802 0.000265 12.006
HMC 50.0 5.036 0.000173 14.471
SMC 2.1 1.973 0.0593 0.855
SMC 2.5 2.502 0.0202 1.301
SMC 3.0 1.586 0.127 0.799
SMC 4.0 2.125 0.0426 0.797
SMC 10.0 2.003 0.0582 1.125
SMC 50.0 -0.912 0.37 -0.302
Metro 2.1 2.954 0.00901 2.557
Metro 2.5 4.153 0.000931 9.858
Metro 3.0 1.319 0.208 11.944
Metro 4.0 3.913 0.00145 6.997
Metro 10.0 5.427 7.95e-05 10.979
Metro 50.0 5.190 8.04e-05 4.629
DEMetro_Z 2.1 3.706 0.00162 2.680
DEMetro_Z 2.5 4.158 0.000702 3.777
DEMetro_Z 3.0 4.093 0.000932 5.153
DEMetro_Z 4.0 5.624 4.51e-05 6.913
DEMetro_Z 10.0 6.955 5.25e-06 11.905
DEMetro_Z 50.0 3.569 0.00283 5.297
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.708 0.11 -0.441
HMC_vs_DEMetro_Z 1 0.473 0.643 0.122
HMC_vs_DEMetro_Z 2 -0.465 0.649 -0.120
HMC_vs_DEMetro_Z 3 -0.895 0.386 -0.231
HMC_vs_DEMetro_Z 4 0.044 0.966 0.011
HMC_vs_DEMetro_Z 5 3.028 0.00903 0.782
Metro_vs_SMC 0 1.920 0.0755 0.496
Metro_vs_SMC 1 3.565 0.00311 0.920
Metro_vs_SMC 2 1.222 0.242 0.315
Metro_vs_SMC 3 3.468 0.00377 0.895
Metro_vs_SMC 4 4.817 0.000274 1.244
Metro_vs_SMC 5 6.267 2.07e-05 1.618
Metro_vs_DEMetro_Z 0 -0.119 0.907 -0.031
Metro_vs_DEMetro_Z 1 2.287 0.0383 0.591
Metro_vs_DEMetro_Z 2 0.767 0.456 0.198
Metro_vs_DEMetro_Z 3 0.042 0.967 0.011
Metro_vs_DEMetro_Z 4 -0.394 0.7 -0.102
Metro_vs_DEMetro_Z 5 -0.400 0.695 -0.103
HMC_vs_Metro 0 -1.058 0.308 -0.273
HMC_vs_Metro 1 -2.181 0.0467 -0.563
HMC_vs_Metro 2 -0.826 0.423 -0.213
HMC_vs_Metro 3 -0.547 0.593 -0.141
HMC_vs_Metro 4 0.306 0.764 0.079
HMC_vs_Metro 5 3.044 0.00876 0.786
HMC_vs_SMC 0 0.836 0.417 0.216
HMC_vs_SMC 1 3.423 0.00412 0.884
HMC_vs_SMC 2 3.489 0.00361 0.901
HMC_vs_SMC 3 5.534 7.36e-05 1.429
HMC_vs_SMC 4 4.476 0.000523 1.156
HMC_vs_SMC 5 5.197 0.000135 1.342
DEMetro_Z_vs_SMC 0 3.135 0.00731 0.809
DEMetro_Z_vs_SMC 1 2.722 0.0165 0.703
DEMetro_Z_vs_SMC 2 3.081 0.00814 0.795
DEMetro_Z_vs_SMC 3 4.769 0.000299 1.231
DEMetro_Z_vs_SMC 4 7.039 5.87e-06 1.818
DEMetro_Z_vs_SMC 5 3.652 0.00262 0.943
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.125 0.059 0.048 1.367
HMC 2.5 0.133 0.035 0.023 4.264
HMC 3.0 0.108 0.028 0.019 4.315
HMC 4.0 0.108 0.024 0.015 5.812
HMC 10.0 0.112 0.017 0.008 12.006
HMC 50.0 0.284 0.032 0.017 14.471
SMC 2.1 0.100 0.059 0.048 0.855
SMC 2.5 0.065 0.035 0.023 1.301
SMC 3.0 0.043 0.028 0.019 0.799
SMC 4.0 0.035 0.024 0.015 0.797
SMC 10.0 0.026 0.017 0.008 1.125
SMC 50.0 0.026 0.032 0.017 -0.302
Metro 2.1 0.182 0.059 0.048 2.557
Metro 2.5 0.261 0.035 0.023 9.858
Metro 3.0 0.251 0.028 0.019 11.944
Metro 4.0 0.126 0.024 0.015 6.997
Metro 10.0 0.104 0.017 0.008 10.979
Metro 50.0 0.112 0.032 0.017 4.629
DEMetro_Z 2.1 0.188 0.059 0.048 2.680
DEMetro_Z 2.5 0.121 0.035 0.023 3.777
DEMetro_Z 3.0 0.124 0.028 0.019 5.153
DEMetro_Z 4.0 0.124 0.024 0.015 6.913
DEMetro_Z 10.0 0.111 0.017 0.008 11.905
DEMetro_Z 50.0 0.124 0.032 0.017 5.297
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.965 0.349 -0.258
HMC 2.5 1.138 0.27 0.808
HMC 3.0 2.089 0.0487 1.135
HMC 4.0 2.238 0.0359 1.220
HMC 10.0 2.140 0.0432 1.064
HMC 50.0 3.169 0.0065 5.319
SMC 2.1 -0.872 0.397 -0.227
SMC 2.5 1.609 0.125 1.197
SMC 3.0 0.563 0.578 0.210
SMC 4.0 -1.222 0.233 -0.381
SMC 10.0 0.320 0.751 0.109
SMC 50.0 0.425 0.674 0.148
Metro 2.1 -1.155 0.267 -0.299
Metro 2.5 1.985 0.0646 2.028
Metro 3.0 1.123 0.28 25.260
Metro 4.0 2.969 0.00835 2.244
Metro 10.0 3.554 0.00219 2.442
Metro 50.0 4.660 0.000254 4.454
DEMetro_Z 2.1 -0.785 0.444 -0.213
DEMetro_Z 2.5 1.343 0.198 1.270
DEMetro_Z 3.0 4.585 0.000194 2.911
DEMetro_Z 4.0 2.604 0.0162 1.373
DEMetro_Z 10.0 3.744 0.00159 3.005
DEMetro_Z 50.0 3.987 0.00081 2.680
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.438 0.668 -0.113
HMC_vs_SMC 1 -0.898 0.384 -0.232
HMC_vs_SMC 2 1.886 0.0802 0.487
HMC_vs_SMC 3 3.465 0.00379 0.895
HMC_vs_SMC 4 2.470 0.027 0.638
HMC_vs_SMC 5 3.005 0.00945 0.776
Metro_vs_DEMetro_Z 0 -1.046 0.313 -0.270
Metro_vs_DEMetro_Z 1 1.474 0.162 0.381
Metro_vs_DEMetro_Z 2 0.987 0.341 0.255
Metro_vs_DEMetro_Z 3 0.988 0.34 0.255
Metro_vs_DEMetro_Z 4 -0.562 0.583 -0.145
Metro_vs_DEMetro_Z 5 1.444 0.171 0.373
HMC_vs_Metro 0 0.589 0.565 0.152
HMC_vs_Metro 1 -2.016 0.0634 -0.521
HMC_vs_Metro 2 -1.070 0.303 -0.276
HMC_vs_Metro 3 -1.107 0.287 -0.286
HMC_vs_Metro 4 -1.651 0.121 -0.426
HMC_vs_Metro 5 0.490 0.632 0.126
HMC_vs_DEMetro_Z 0 -0.414 0.685 -0.107
HMC_vs_DEMetro_Z 1 -1.065 0.305 -0.275
HMC_vs_DEMetro_Z 2 -2.747 0.0157 -0.709
HMC_vs_DEMetro_Z 3 -0.240 0.814 -0.062
HMC_vs_DEMetro_Z 4 -2.273 0.0393 -0.587
HMC_vs_DEMetro_Z 5 1.413 0.179 0.365
Metro_vs_SMC 0 -1.974 0.0684 -0.510
Metro_vs_SMC 1 1.344 0.2 0.347
Metro_vs_SMC 2 1.110 0.286 0.287
Metro_vs_SMC 3 3.536 0.00329 0.913
Metro_vs_SMC 4 3.113 0.00763 0.804
Metro_vs_SMC 5 4.647 0.000377 1.200
DEMetro_Z_vs_SMC 0 0.174 0.864 0.045
DEMetro_Z_vs_SMC 1 0.160 0.875 0.041
DEMetro_Z_vs_SMC 2 5.089 0.000165 1.314
DEMetro_Z_vs_SMC 3 3.422 0.00413 0.884
DEMetro_Z_vs_SMC 4 3.615 0.00281 0.933
DEMetro_Z_vs_SMC 5 4.052 0.00119 1.046
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.352 17.910 44.869 -0.258
HMC 2.5 1.920 1.151 0.952 0.808
HMC 3.0 0.508 0.268 0.211 1.135
HMC 4.0 0.281 0.163 0.097 1.220
HMC 10.0 0.089 0.049 0.038 1.064
HMC 50.0 0.184 0.042 0.027 5.319
SMC 2.1 7.743 17.910 44.869 -0.227
SMC 2.5 2.291 1.151 0.952 1.197
SMC 3.0 0.312 0.268 0.211 0.210
SMC 4.0 0.126 0.163 0.097 -0.381
SMC 10.0 0.053 0.049 0.038 0.109
SMC 50.0 0.046 0.042 0.027 0.148
Metro 2.1 4.490 17.910 44.869 -0.299
Metro 2.5 3.081 1.151 0.952 2.028
Metro 3.0 5.606 0.268 0.211 25.260
Metro 4.0 0.380 0.163 0.097 2.244
Metro 10.0 0.140 0.049 0.038 2.442
Metro 50.0 0.161 0.042 0.027 4.454
DEMetro_Z 2.1 8.368 17.910 44.869 -0.213
DEMetro_Z 2.5 2.359 1.151 0.952 1.270
DEMetro_Z 3.0 0.883 0.268 0.211 2.911
DEMetro_Z 4.0 0.295 0.163 0.097 1.373
DEMetro_Z 10.0 0.161 0.049 0.038 3.005
DEMetro_Z 50.0 0.114 0.042 0.027 2.680
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.802 0.00103 2.109
HMC 2.5 5.561 4.97e-05 6.613
HMC 3.0 7.116 2.34e-06 6.888
HMC 4.0 6.783 5.55e-06 8.277
HMC 10.0 4.920 0.00022 18.683
HMC 50.0 5.022 0.000183 21.456
SMC 2.1 7.005 2.97e-06 6.992
SMC 2.5 5.534 4.96e-05 6.119
SMC 3.0 2.762 0.0123 1.766
SMC 4.0 2.001 0.0554 0.795
SMC 10.0 1.343 0.195 0.867
SMC 50.0 -0.853 0.401 -0.285
Metro 2.1 7.033 3.11e-07 3.401
Metro 2.5 5.528 7.04e-05 16.428
Metro 3.0 1.675 0.116 23.594
Metro 4.0 4.717 0.000314 12.337
Metro 10.0 6.517 1.26e-05 18.898
Metro 50.0 6.838 4.89e-06 8.087
DEMetro_Z 2.1 3.817 0.00168 5.306
DEMetro_Z 2.5 9.776 3.03e-08 8.980
DEMetro_Z 3.0 6.743 6.63e-06 9.423
DEMetro_Z 4.0 6.209 1.94e-05 11.876
DEMetro_Z 10.0 9.893 8.06e-08 20.348
DEMetro_Z 50.0 4.116 0.000981 8.229
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.412 0.18 -0.364
Metro_vs_DEMetro_Z 1 2.278 0.039 0.588
Metro_vs_DEMetro_Z 2 1.025 0.323 0.265
Metro_vs_DEMetro_Z 3 0.138 0.892 0.036
Metro_vs_DEMetro_Z 4 -0.430 0.674 -0.111
Metro_vs_DEMetro_Z 5 -0.062 0.951 -0.016
DEMetro_Z_vs_SMC 0 -1.138 0.274 -0.294
DEMetro_Z_vs_SMC 1 2.058 0.0587 0.531
DEMetro_Z_vs_SMC 2 4.981 0.000202 1.286
DEMetro_Z_vs_SMC 3 5.767 4.87e-05 1.489
DEMetro_Z_vs_SMC 4 9.885 1.08e-07 2.552
DEMetro_Z_vs_SMC 5 4.200 0.000891 1.084
HMC_vs_DEMetro_Z 0 -2.165 0.0482 -0.559
HMC_vs_DEMetro_Z 1 -1.862 0.0837 -0.481
HMC_vs_DEMetro_Z 2 -1.233 0.238 -0.318
HMC_vs_DEMetro_Z 3 -1.958 0.0705 -0.505
HMC_vs_DEMetro_Z 4 -0.429 0.674 -0.111
HMC_vs_DEMetro_Z 5 2.987 0.00981 0.771
HMC_vs_Metro 0 -1.798 0.0938 -0.464
HMC_vs_Metro 1 -3.012 0.00933 -0.778
HMC_vs_Metro 2 -1.153 0.268 -0.298
HMC_vs_Metro 3 -1.216 0.244 -0.314
HMC_vs_Metro 4 -0.042 0.967 -0.011
HMC_vs_Metro 5 2.786 0.0146 0.719
HMC_vs_SMC 0 -4.557 0.000447 -1.177
HMC_vs_SMC 1 0.373 0.715 0.096
HMC_vs_SMC 2 4.346 0.000672 1.122
HMC_vs_SMC 3 6.484 1.44e-05 1.674
HMC_vs_SMC 4 4.831 0.000267 1.247
HMC_vs_SMC 5 5.117 0.000157 1.321
Metro_vs_SMC 0 -3.873 0.00169 -1.000
Metro_vs_SMC 1 3.408 0.00424 0.880
Metro_vs_SMC 2 1.536 0.147 0.397
Metro_vs_SMC 3 4.301 0.000732 1.110
Metro_vs_SMC 4 6.108 2.7e-05 1.577
Metro_vs_SMC 5 7.853 1.7e-06 2.028
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.229 0.122 0.051 2.109
HMC 2.5 0.171 0.076 0.014 6.613
HMC 3.0 0.138 0.063 0.011 6.888
HMC 4.0 0.122 0.047 0.009 8.277
HMC 10.0 0.116 0.033 0.004 18.683
HMC 50.0 0.272 0.038 0.011 21.456
SMC 2.1 0.476 0.122 0.051 6.992
SMC 2.5 0.164 0.076 0.014 6.119
SMC 3.0 0.082 0.063 0.011 1.766
SMC 4.0 0.054 0.047 0.009 0.795
SMC 10.0 0.036 0.033 0.004 0.867
SMC 50.0 0.035 0.038 0.011 -0.285
Metro 2.1 0.294 0.122 0.051 3.401
Metro 2.5 0.313 0.076 0.014 16.428
Metro 3.0 0.322 0.063 0.011 23.594
Metro 4.0 0.159 0.047 0.009 12.337
Metro 10.0 0.117 0.033 0.004 18.898
Metro 50.0 0.126 0.038 0.011 8.087
DEMetro_Z 2.1 0.391 0.122 0.051 5.306
DEMetro_Z 2.5 0.206 0.076 0.014 8.980
DEMetro_Z 3.0 0.166 0.063 0.011 9.423
DEMetro_Z 4.0 0.155 0.047 0.009 11.876
DEMetro_Z 10.0 0.123 0.033 0.004 20.348
DEMetro_Z 50.0 0.128 0.038 0.011 8.229
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.886 1.35e-05 4.151
HMC 2.5 4.523 0.000401 6.137
HMC 3.0 5.672 3.55e-05 5.790
HMC 4.0 5.114 0.000128 7.183
HMC 10.0 4.794 0.000265 10.565
HMC 50.0 5.112 0.000154 20.397
SMC 2.1 10.973 9.32e-09 11.958
SMC 2.5 6.068 1.72e-05 6.363
SMC 3.0 3.006 0.00714 1.891
SMC 4.0 2.219 0.0357 0.991
SMC 10.0 1.044 0.306 0.461
SMC 50.0 -0.650 0.521 -0.235
Metro 2.1 7.486 6.67e-07 5.539
Metro 2.5 5.493 6.75e-05 9.534
Metro 3.0 5.402 6.78e-05 6.499
Metro 4.0 5.906 2.9e-05 8.269
Metro 10.0 6.007 2.31e-05 7.820
Metro 50.0 6.412 9.35e-06 6.872
DEMetro_Z 2.1 8.836 7.44e-08 6.841
DEMetro_Z 2.5 6.325 1.35e-05 8.654
DEMetro_Z 3.0 5.173 0.000108 6.496
DEMetro_Z 4.0 5.051 0.000162 10.945
DEMetro_Z 10.0 8.212 5.15e-07 9.673
DEMetro_Z 50.0 3.837 0.00172 7.959
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -6.559 1.27e-05 -1.693
DEMetro_Z_vs_SMC 1 1.516 0.152 0.391
DEMetro_Z_vs_SMC 2 3.499 0.00354 0.903
DEMetro_Z_vs_SMC 3 4.497 0.000502 1.161
DEMetro_Z_vs_SMC 4 8.268 9.31e-07 2.135
DEMetro_Z_vs_SMC 5 3.960 0.00142 1.022
HMC_vs_Metro 0 -1.637 0.124 -0.423
HMC_vs_Metro 1 -1.634 0.124 -0.422
HMC_vs_Metro 2 -0.404 0.692 -0.104
HMC_vs_Metro 3 -0.475 0.642 -0.123
HMC_vs_Metro 4 1.024 0.323 0.264
HMC_vs_Metro 5 3.148 0.00712 0.813
Metro_vs_DEMetro_Z 0 -1.418 0.178 -0.366
Metro_vs_DEMetro_Z 1 0.374 0.714 0.097
Metro_vs_DEMetro_Z 2 0.003 0.998 0.001
Metro_vs_DEMetro_Z 3 -0.963 0.352 -0.249
Metro_vs_DEMetro_Z 4 -1.147 0.271 -0.296
Metro_vs_DEMetro_Z 5 -0.479 0.639 -0.124
HMC_vs_SMC 0 -5.784 4.73e-05 -1.494
HMC_vs_SMC 1 -0.139 0.892 -0.036
HMC_vs_SMC 2 3.244 0.00588 0.838
HMC_vs_SMC 3 4.446 0.000553 1.148
HMC_vs_SMC 4 4.604 0.000409 1.189
HMC_vs_SMC 5 5.231 0.000127 1.351
Metro_vs_SMC 0 -5.197 0.000135 -1.342
Metro_vs_SMC 1 1.637 0.124 0.423
Metro_vs_SMC 2 3.481 0.00367 0.899
Metro_vs_SMC 3 5.448 8.59e-05 1.407
Metro_vs_SMC 4 5.718 5.32e-05 1.476
Metro_vs_SMC 5 7.439 3.16e-06 1.921
HMC_vs_DEMetro_Z 0 -2.654 0.0189 -0.685
HMC_vs_DEMetro_Z 1 -1.495 0.157 -0.386
HMC_vs_DEMetro_Z 2 -0.386 0.705 -0.100
HMC_vs_DEMetro_Z 3 -1.719 0.108 -0.444
HMC_vs_DEMetro_Z 4 0.400 0.695 0.103
HMC_vs_DEMetro_Z 5 2.903 0.0116 0.749
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.041 0.013 0.007 4.151
HMC 2.5 0.035 0.013 0.004 6.137
HMC 3.0 0.039 0.014 0.004 5.790
HMC 4.0 0.040 0.012 0.004 7.183
HMC 10.0 0.053 0.011 0.004 10.565
HMC 50.0 0.127 0.015 0.005 20.397
SMC 2.1 0.092 0.013 0.007 11.958
SMC 2.5 0.036 0.013 0.004 6.363
SMC 3.0 0.022 0.014 0.004 1.891
SMC 4.0 0.016 0.012 0.004 0.991
SMC 10.0 0.013 0.011 0.004 0.461
SMC 50.0 0.013 0.015 0.005 -0.235
Metro 2.1 0.050 0.013 0.007 5.539
Metro 2.5 0.048 0.013 0.004 9.534
Metro 3.0 0.043 0.014 0.004 6.499
Metro 4.0 0.044 0.012 0.004 8.269
Metro 10.0 0.042 0.011 0.004 7.820
Metro 50.0 0.052 0.015 0.005 6.872
DEMetro_Z 2.1 0.059 0.013 0.007 6.841
DEMetro_Z 2.5 0.044 0.013 0.004 8.654
DEMetro_Z 3.0 0.042 0.014 0.004 6.496
DEMetro_Z 4.0 0.054 0.012 0.004 10.945
DEMetro_Z 10.0 0.049 0.011 0.004 9.673
DEMetro_Z 50.0 0.058 0.015 0.005 7.959
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.502 0.144 0.516
HMC 2.5 3.705 0.00183 3.291
HMC 3.0 4.004 0.00107 4.464
HMC 4.0 3.824 0.00156 4.284
HMC 10.0 6.304 1.75e-05 15.215
HMC 50.0 7.764 1.77e-06 23.555
SMC 2.1 2.820 0.00894 1.166
SMC 2.5 2.715 0.0126 1.433
SMC 3.0 0.747 0.461 0.263
SMC 4.0 2.452 0.0219 1.176
SMC 10.0 0.892 0.383 0.501
SMC 50.0 -1.322 0.197 -0.503
Metro 2.1 2.277 0.0385 4.793
Metro 2.5 5.101 9.45e-05 4.454
Metro 3.0 4.972 0.000164 6.608
Metro 4.0 4.570 0.000394 8.235
Metro 10.0 4.552 0.000425 10.436
Metro 50.0 3.613 0.00246 4.235
DEMetro_Z 2.1 3.538 0.00213 2.217
DEMetro_Z 2.5 3.039 0.00835 4.503
DEMetro_Z 3.0 3.066 0.00767 3.662
DEMetro_Z 4.0 3.127 0.00698 4.682
DEMetro_Z 10.0 3.854 0.00164 7.195
DEMetro_Z 50.0 2.732 0.0156 4.281
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.450 0.00391 -0.891
HMC_vs_DEMetro_Z 1 -0.808 0.432 -0.209
HMC_vs_DEMetro_Z 2 0.394 0.7 0.102
HMC_vs_DEMetro_Z 3 -0.265 0.795 -0.068
HMC_vs_DEMetro_Z 4 2.287 0.0383 0.591
HMC_vs_DEMetro_Z 5 5.516 7.6e-05 1.424
Metro_vs_SMC 0 1.697 0.112 0.438
Metro_vs_SMC 1 3.031 0.00898 0.783
Metro_vs_SMC 2 4.915 0.000228 1.269
Metro_vs_SMC 3 3.583 0.003 0.925
Metro_vs_SMC 4 3.977 0.00138 1.027
Metro_vs_SMC 5 3.869 0.0017 0.999
Metro_vs_DEMetro_Z 0 1.171 0.261 0.302
Metro_vs_DEMetro_Z 1 -0.026 0.979 -0.007
Metro_vs_DEMetro_Z 2 1.553 0.143 0.401
Metro_vs_DEMetro_Z 3 1.301 0.214 0.336
Metro_vs_DEMetro_Z 4 1.451 0.169 0.375
Metro_vs_DEMetro_Z 5 -0.028 0.978 -0.007
HMC_vs_Metro 0 -2.035 0.0613 -0.525
HMC_vs_Metro 1 -0.846 0.412 -0.218
HMC_vs_Metro 2 -1.348 0.199 -0.348
HMC_vs_Metro 3 -1.801 0.0933 -0.465
HMC_vs_Metro 4 1.514 0.152 0.391
HMC_vs_Metro 5 6.980 6.45e-06 1.802
HMC_vs_SMC 0 -1.616 0.128 -0.417
HMC_vs_SMC 1 1.628 0.126 0.420
HMC_vs_SMC 2 3.925 0.00153 1.013
HMC_vs_SMC 3 2.545 0.0233 0.657
HMC_vs_SMC 4 5.807 4.55e-05 1.499
HMC_vs_SMC 5 7.552 2.66e-06 1.950
DEMetro_Z_vs_SMC 0 1.541 0.145 0.398
DEMetro_Z_vs_SMC 1 2.202 0.045 0.568
DEMetro_Z_vs_SMC 2 2.866 0.0125 0.740
DEMetro_Z_vs_SMC 3 2.783 0.0147 0.718
DEMetro_Z_vs_SMC 4 3.785 0.00201 0.977
DEMetro_Z_vs_SMC 5 3.191 0.00654 0.824
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.084 0.059 0.048 0.516
HMC 2.5 0.110 0.035 0.023 3.291
HMC 3.0 0.111 0.028 0.019 4.464
HMC 4.0 0.086 0.024 0.015 4.284
HMC 10.0 0.137 0.017 0.008 15.215
HMC 50.0 0.443 0.032 0.017 23.555
SMC 2.1 0.115 0.059 0.048 1.166
SMC 2.5 0.068 0.035 0.023 1.433
SMC 3.0 0.033 0.028 0.019 0.263
SMC 4.0 0.041 0.024 0.015 1.176
SMC 10.0 0.021 0.017 0.008 0.501
SMC 50.0 0.023 0.032 0.017 -0.503
Metro 2.1 0.290 0.059 0.048 4.793
Metro 2.5 0.137 0.035 0.023 4.454
Metro 3.0 0.151 0.028 0.019 6.608
Metro 4.0 0.144 0.024 0.015 8.235
Metro 10.0 0.100 0.017 0.008 10.436
Metro 50.0 0.105 0.032 0.017 4.235
DEMetro_Z 2.1 0.166 0.059 0.048 2.217
DEMetro_Z 2.5 0.138 0.035 0.023 4.503
DEMetro_Z 3.0 0.096 0.028 0.019 3.662
DEMetro_Z 4.0 0.092 0.024 0.015 4.682
DEMetro_Z 10.0 0.074 0.017 0.008 7.195
DEMetro_Z 50.0 0.106 0.032 0.017 4.281
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.244 0.234 -0.322
HMC 2.5 1.128 0.276 1.069
HMC 3.0 1.781 0.0954 2.753
HMC 4.0 1.767 0.0938 1.233
HMC 10.0 3.532 0.00173 1.703
HMC 50.0 4.929 0.000206 11.133
SMC 2.1 -1.173 0.26 -0.303
SMC 2.5 1.048 0.31 0.949
SMC 3.0 0.083 0.934 0.029
SMC 4.0 -1.899 0.0701 -0.576
SMC 10.0 0.822 0.418 0.284
SMC 50.0 -0.394 0.697 -0.141
Metro 2.1 -0.880 0.392 -0.237
Metro 2.5 1.062 0.303 0.854
Metro 3.0 3.674 0.00213 4.087
Metro 4.0 2.725 0.0158 4.025
Metro 10.0 4.533 0.000333 4.396
Metro 50.0 4.300 0.000589 4.924
DEMetro_Z 2.1 -1.162 0.264 -0.301
DEMetro_Z 2.5 1.728 0.103 1.566
DEMetro_Z 3.0 3.987 0.000953 3.291
DEMetro_Z 4.0 3.282 0.00474 3.411
DEMetro_Z 10.0 4.279 0.00036 2.543
DEMetro_Z 50.0 3.979 0.000955 3.209
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.993 0.337 -0.256
HMC_vs_SMC 1 0.330 0.747 0.085
HMC_vs_SMC 2 1.750 0.102 0.452
HMC_vs_SMC 3 2.526 0.0242 0.652
HMC_vs_SMC 4 3.562 0.00313 0.920
HMC_vs_SMC 5 4.876 0.000245 1.259
Metro_vs_DEMetro_Z 0 1.067 0.304 0.276
Metro_vs_DEMetro_Z 1 -1.698 0.112 -0.438
Metro_vs_DEMetro_Z 2 0.588 0.566 0.152
Metro_vs_DEMetro_Z 3 0.347 0.734 0.090
Metro_vs_DEMetro_Z 4 1.525 0.15 0.394
Metro_vs_DEMetro_Z 5 1.341 0.201 0.346
HMC_vs_Metro 0 -1.302 0.214 -0.336
HMC_vs_Metro 1 0.517 0.613 0.133
HMC_vs_Metro 2 -0.700 0.495 -0.181
HMC_vs_Metro 3 -1.831 0.0885 -0.473
HMC_vs_Metro 4 -2.523 0.0244 -0.651
HMC_vs_Metro 5 3.327 0.00499 0.859
HMC_vs_DEMetro_Z 0 -2.161 0.0485 -0.558
HMC_vs_DEMetro_Z 1 -0.888 0.39 -0.229
HMC_vs_DEMetro_Z 2 -0.328 0.748 -0.085
HMC_vs_DEMetro_Z 3 -3.212 0.00626 -0.829
HMC_vs_DEMetro_Z 4 -1.993 0.0661 -0.515
HMC_vs_DEMetro_Z 5 3.466 0.00378 0.895
Metro_vs_SMC 0 0.862 0.403 0.223
Metro_vs_SMC 1 -0.232 0.82 -0.060
Metro_vs_SMC 2 3.779 0.00203 0.976
Metro_vs_SMC 3 3.152 0.00707 0.814
Metro_vs_SMC 4 4.876 0.000245 1.259
Metro_vs_SMC 5 4.043 0.00121 1.044
DEMetro_Z_vs_SMC 0 0.088 0.931 0.023
DEMetro_Z_vs_SMC 1 1.111 0.285 0.287
DEMetro_Z_vs_SMC 2 4.789 0.000289 1.236
DEMetro_Z_vs_SMC 3 3.855 0.00175 0.995
DEMetro_Z_vs_SMC 4 3.965 0.00141 1.024
DEMetro_Z_vs_SMC 5 4.151 0.00098 1.072
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 3.473 17.910 44.869 -0.322
HMC 2.5 2.169 1.151 0.952 1.069
HMC 3.0 0.850 0.268 0.211 2.753
HMC 4.0 0.282 0.163 0.097 1.233
HMC 10.0 0.113 0.049 0.038 1.703
HMC 50.0 0.340 0.042 0.027 11.133
SMC 2.1 4.303 17.910 44.869 -0.303
SMC 2.5 2.054 1.151 0.952 0.949
SMC 3.0 0.274 0.268 0.211 0.029
SMC 4.0 0.107 0.163 0.097 -0.576
SMC 10.0 0.059 0.049 0.038 0.284
SMC 50.0 0.038 0.042 0.027 -0.141
Metro 2.1 7.266 17.910 44.869 -0.237
Metro 2.5 1.964 1.151 0.952 0.854
Metro 3.0 1.132 0.268 0.211 4.087
Metro 4.0 0.552 0.163 0.097 4.025
Metro 10.0 0.214 0.049 0.038 4.396
Metro 50.0 0.174 0.042 0.027 4.924
DEMetro_Z 2.1 4.402 17.910 44.869 -0.301
DEMetro_Z 2.5 2.641 1.151 0.952 1.566
DEMetro_Z 3.0 0.963 0.268 0.211 3.291
DEMetro_Z 4.0 0.493 0.163 0.097 3.411
DEMetro_Z 10.0 0.144 0.049 0.038 2.543
DEMetro_Z 50.0 0.128 0.042 0.027 3.209
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.838 0.0768 0.655
HMC 2.5 6.023 1.87e-05 6.308
HMC 3.0 4.510 0.000446 8.349
HMC 4.0 4.817 0.000225 6.582
HMC 10.0 6.877 7.12e-06 22.630
HMC 50.0 7.851 1.63e-06 34.148
SMC 2.1 8.144 5.38e-08 4.459
SMC 2.5 3.932 0.00123 4.241
SMC 3.0 -0.018 0.986 -0.008
SMC 4.0 2.422 0.0237 1.210
SMC 10.0 1.445 0.164 0.863
SMC 50.0 -1.133 0.267 -0.414
Metro 2.1 2.509 0.0247 5.803
Metro 2.5 11.419 2.53e-09 9.816
Metro 3.0 8.878 2.34e-07 12.336
Metro 4.0 6.973 5.4e-06 13.663
Metro 10.0 6.418 1.5e-05 19.608
Metro 50.0 5.460 6.74e-05 7.965
DEMetro_Z 2.1 5.905 4.75e-06 2.890
DEMetro_Z 2.5 5.901 3.17e-05 9.841
DEMetro_Z 3.0 7.007 3.58e-06 8.105
DEMetro_Z 4.0 5.710 4.61e-05 10.360
DEMetro_Z 10.0 6.888 6.38e-06 14.626
DEMetro_Z 50.0 3.807 0.00182 7.398
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.255 0.23 0.324
Metro_vs_DEMetro_Z 1 -0.015 0.988 -0.004
Metro_vs_DEMetro_Z 2 2.229 0.0427 0.576
Metro_vs_DEMetro_Z 3 1.113 0.284 0.287
Metro_vs_DEMetro_Z 4 1.500 0.156 0.387
Metro_vs_DEMetro_Z 5 0.239 0.815 0.062
DEMetro_Z_vs_SMC 0 -2.059 0.0586 -0.532
DEMetro_Z_vs_SMC 1 3.040 0.00883 0.785
DEMetro_Z_vs_SMC 2 7.109 5.26e-06 1.836
DEMetro_Z_vs_SMC 3 5.559 7.04e-05 1.435
DEMetro_Z_vs_SMC 4 7.001 6.24e-06 1.808
DEMetro_Z_vs_SMC 5 4.170 0.000944 1.077
HMC_vs_DEMetro_Z 0 -4.586 0.000424 -1.184
HMC_vs_DEMetro_Z 1 -1.817 0.0906 -0.469
HMC_vs_DEMetro_Z 2 0.092 0.928 0.024
HMC_vs_DEMetro_Z 3 -1.947 0.0719 -0.503
HMC_vs_DEMetro_Z 4 1.727 0.106 0.446
HMC_vs_DEMetro_Z 5 5.456 8.47e-05 1.409
HMC_vs_Metro 0 -2.293 0.0379 -0.592
HMC_vs_Metro 1 -2.499 0.0255 -0.645
HMC_vs_Metro 2 -1.684 0.114 -0.435
HMC_vs_Metro 3 -2.780 0.0148 -0.718
HMC_vs_Metro 4 0.685 0.504 0.177
HMC_vs_Metro 5 6.513 1.37e-05 1.682
HMC_vs_SMC 0 -7.979 1.41e-06 -2.060
HMC_vs_SMC 1 1.513 0.152 0.391
HMC_vs_SMC 2 4.536 0.000466 1.171
HMC_vs_SMC 3 3.620 0.00278 0.935
HMC_vs_SMC 4 6.368 1.75e-05 1.644
HMC_vs_SMC 5 7.667 2.24e-06 1.980
Metro_vs_SMC 0 0.573 0.576 0.148
Metro_vs_SMC 1 3.951 0.00145 1.020
Metro_vs_SMC 2 8.939 3.68e-07 2.308
Metro_vs_SMC 3 6.115 2.67e-05 1.579
Metro_vs_SMC 4 5.814 4.49e-05 1.501
Metro_vs_SMC 5 5.554 7.1e-05 1.434
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.155 0.122 0.051 0.655
HMC 2.5 0.167 0.076 0.014 6.308
HMC 3.0 0.154 0.063 0.011 8.349
HMC 4.0 0.107 0.047 0.009 6.582
HMC 10.0 0.133 0.033 0.004 22.630
HMC 50.0 0.410 0.038 0.011 34.148
SMC 2.1 0.348 0.122 0.051 4.459
SMC 2.5 0.137 0.076 0.014 4.241
SMC 3.0 0.063 0.063 0.011 -0.008
SMC 4.0 0.058 0.047 0.009 1.210
SMC 10.0 0.036 0.033 0.004 0.863
SMC 50.0 0.034 0.038 0.011 -0.414
Metro 2.1 0.416 0.122 0.051 5.803
Metro 2.5 0.218 0.076 0.014 9.816
Metro 3.0 0.198 0.063 0.011 12.336
Metro 4.0 0.171 0.047 0.009 13.663
Metro 10.0 0.120 0.033 0.004 19.608
Metro 50.0 0.125 0.038 0.011 7.965
DEMetro_Z 2.1 0.268 0.122 0.051 2.890
DEMetro_Z 2.5 0.218 0.076 0.014 9.841
DEMetro_Z 3.0 0.152 0.063 0.011 8.105
DEMetro_Z 4.0 0.141 0.047 0.009 10.360
DEMetro_Z 10.0 0.098 0.033 0.004 14.626
DEMetro_Z 50.0 0.119 0.038 0.011 7.398
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.715 0.00122 1.979
HMC 2.5 5.283 8.27e-05 6.064
HMC 3.0 4.058 0.00105 6.080
HMC 4.0 4.278 0.000641 5.416
HMC 10.0 6.558 1.04e-05 11.738
HMC 50.0 7.381 3.32e-06 32.459
SMC 2.1 9.487 5.11e-08 9.059
SMC 2.5 3.788 0.00166 4.054
SMC 3.0 0.034 0.973 0.013
SMC 4.0 2.240 0.0351 1.123
SMC 10.0 0.888 0.382 0.338
SMC 50.0 -0.861 0.397 -0.337
Metro 2.1 7.720 3.5e-07 5.344
Metro 2.5 6.622 7.59e-06 8.407
Metro 3.0 7.875 4.9e-07 6.714
Metro 4.0 7.191 2.62e-06 8.333
Metro 10.0 5.288 9.38e-05 7.887
Metro 50.0 5.508 5.42e-05 6.433
DEMetro_Z 2.1 5.154 7.88e-05 4.223
DEMetro_Z 2.5 5.944 2.48e-05 7.264
DEMetro_Z 3.0 4.911 0.00016 5.050
DEMetro_Z 4.0 4.267 0.000719 7.888
DEMetro_Z 10.0 7.882 3.77e-07 6.120
DEMetro_Z 50.0 3.248 0.00564 6.880
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -3.459 0.00384 -0.893
DEMetro_Z_vs_SMC 1 2.848 0.0129 0.735
DEMetro_Z_vs_SMC 2 5.055 0.000176 1.305
DEMetro_Z_vs_SMC 3 4.223 0.000852 1.090
DEMetro_Z_vs_SMC 4 7.099 5.35e-06 1.833
DEMetro_Z_vs_SMC 5 3.472 0.00374 0.896
HMC_vs_Metro 0 -3.995 0.00133 -1.031
HMC_vs_Metro 1 -1.441 0.171 -0.372
HMC_vs_Metro 2 -0.333 0.744 -0.086
HMC_vs_Metro 3 -1.467 0.165 -0.379
HMC_vs_Metro 4 1.758 0.101 0.454
HMC_vs_Metro 5 6.425 1.59e-05 1.659
Metro_vs_DEMetro_Z 0 1.369 0.193 0.353
Metro_vs_DEMetro_Z 1 0.746 0.468 0.193
Metro_vs_DEMetro_Z 2 1.477 0.162 0.381
Metro_vs_DEMetro_Z 3 0.190 0.852 0.049
Metro_vs_DEMetro_Z 4 1.294 0.217 0.334
Metro_vs_DEMetro_Z 5 -0.205 0.84 -0.053
HMC_vs_SMC 0 -7.695 2.15e-06 -1.987
HMC_vs_SMC 1 1.311 0.211 0.339
HMC_vs_SMC 2 3.875 0.00168 1.000
HMC_vs_SMC 3 3.260 0.00569 0.842
HMC_vs_SMC 4 6.547 1.3e-05 1.690
HMC_vs_SMC 5 7.194 4.61e-06 1.858
Metro_vs_SMC 0 -3.012 0.00933 -0.778
Metro_vs_SMC 1 3.334 0.00492 0.861
Metro_vs_SMC 2 9.153 2.77e-07 2.363
Metro_vs_SMC 3 5.610 6.43e-05 1.448
Metro_vs_SMC 4 4.981 0.000202 1.286
Metro_vs_SMC 5 5.337 0.000105 1.378
HMC_vs_DEMetro_Z 0 -2.282 0.0387 -0.589
HMC_vs_DEMetro_Z 1 -0.792 0.442 -0.204
HMC_vs_DEMetro_Z 2 0.460 0.652 0.119
HMC_vs_DEMetro_Z 3 -1.181 0.257 -0.305
HMC_vs_DEMetro_Z 4 2.754 0.0155 0.711
HMC_vs_DEMetro_Z 5 5.225 0.000129 1.349
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.027 0.013 0.007 1.979
HMC 2.5 0.035 0.013 0.004 6.064
HMC 3.0 0.041 0.014 0.004 6.080
HMC 4.0 0.033 0.012 0.004 5.416
HMC 10.0 0.057 0.011 0.004 11.738
HMC 50.0 0.193 0.015 0.005 32.459
SMC 2.1 0.073 0.013 0.007 9.059
SMC 2.5 0.028 0.013 0.004 4.054
SMC 3.0 0.014 0.014 0.004 0.013
SMC 4.0 0.017 0.012 0.004 1.123
SMC 10.0 0.013 0.011 0.004 0.338
SMC 50.0 0.013 0.015 0.005 -0.337
Metro 2.1 0.049 0.013 0.007 5.344
Metro 2.5 0.044 0.013 0.004 8.407
Metro 3.0 0.043 0.014 0.004 6.714
Metro 4.0 0.044 0.012 0.004 8.333
Metro 10.0 0.042 0.011 0.004 7.887
Metro 50.0 0.050 0.015 0.005 6.433
DEMetro_Z 2.1 0.041 0.013 0.007 4.223
DEMetro_Z 2.5 0.039 0.013 0.004 7.264
DEMetro_Z 3.0 0.036 0.014 0.004 5.050
DEMetro_Z 4.0 0.042 0.012 0.004 7.888
DEMetro_Z 10.0 0.035 0.011 0.004 6.120
DEMetro_Z 50.0 0.052 0.015 0.005 6.880
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50